Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling

Data Handling Exercise 21A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Consider the following numbers :
68, 76, 63, 75, 93, 83, 70, 115, 82, 105, 90, 103, 92, 52, 99, 73, 75, 63, 77 and 71.
(i) Arrange these numbers in ascending order.
(ii) What the range of these numbers?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 1

Question 2.
Represent the following data in the form of a frequency distribution table :
16, 17, 21, 20, 16, 20, 16, 18, 17, 21, 17, 18, 19, 17, 15, 15, 19, 19, 18, 17, 17, 15, 15, 16, 17, 17, 19, 18, 17, 16, 15, 20, 16, 17, 19, 18, 19, 16, 21 and 17.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 2

Question 3.
A die was thrown 20 times and following scores were recorded.
2, 1, 5, 2, 4, 3, 6, 1, 4, 2, 5, 1, 6, 2, 6, 3, 5, 4, 1 and 3.
Prepare a frequency table for the scores.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 3

Question 4.
Following data shows the weekly wages (in ₹) of 10 workers in a factory.
3500, 4250, 4000, 4250, 4000, 3750, 4750, 4000, 4250 and 4000
(i) Prepare a frequency distribution table.
(ii) What is the range of wages (in ₹)?
(iii) How many workers are getting the maximum wages?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 4

Question 5.
The marks obtained by 40 students of a class are given below :
80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40,20, 80, 90, 50, 80, 60, 70, 40, 50, 60, 90, 60, 40, 40, 60 and 60
(i) Construct a frequency distribution table.
(ii) Find how many students have marks equal to or more than 70?
(iii) How many students obtained marks below 40?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 5

Question 6.
Arrange the following data in descending order:
3.3, 3.2, 3.1, 3.7, 3.6, 4.0, 3.5, 3.9, 3.8, 4.1, 3.5, 3.8, 3.7, 3.9 and 3.4.
(i) Determine the range.
(ii) How many numbers are less than 3.5?
(iii) How many numbers are 3.8 or above?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21A 6

Data Handling Exercise 21B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the mean of 53, 61, 60, 67 and 64.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 7

Question 2.
Find the mean of first six natural numbers.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 8

Question 3.
Find the mean of first ten odd natural numbers.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 9

Question 4.
Find the mean of all factors of 10.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 10

Question 5.
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 11

Question 6.
If different values of variable x are 19.8,15.4,13.7,11.71,11.8, 12.6,12.8,18.6,20.5 and 2.1, find the mean.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 12

Question 7.
The mean of a certain number of observations is 32. Find the resulting mean, if each observation is,
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 13
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 14

Question 8.
The pocket expenses (per day) of Anuj, during a certain week, from monday to Saturday were ₹85.40, ₹88.00, ₹86.50, ₹84.75, ₹82.60 and ₹87.25. Find the mean pocket expenses per day.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 15

Question 9.
If the mean of 8, 10, 7, x + 2 and 6 is 9, find the value of x.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 16

Question 10.
Find the mean of first six multiples of 3.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 17

Question 11.
Find the mean of first five prime numbers.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 18

Question 12.
The mean of six numbers :x-5,x- 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 19

Question 13.
Find the mean of squares of first five whole numbers.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 20

Question 14.
If the mean of 6, 4, 7, p and 10 is 8, find the value of p.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 21

Question 15.
Find the mean of first six multiples of 5.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 22

Question 16.
The rainfall (in mm) in a city on 7 days of a certain week is recorded as follows
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B Q16
Find the total and average (mean) rainfall for the week.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 23

Question 17.
The mean of marks scored by 100 students was found to be 40, later on it was discovered that a score of 53 was misread as 83. Find the correct mean.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 24

Question 18.
The mean of five numbers is 27. If one number is excluded, the mean of remaining numbers is 25. Find the excluded number.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 25

Question 19.
The mean of 5 numbers is 27. If one new number is included, the new mean is 25. Find the included number.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 26

Question 20.
Mean of 5 numbers is 20 and mean of other 5 numbers is 30. Find the mean of all the 10 numbers taken together.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 27

Question 21.
Find the median of:
(i) 5,7, 9, 11, 15, 17,2, 23 and 19
(ii) 9, 3, 20, 13, 0, 7 and 10
(iii) 18, 19, 20, 23, 22, 20, 17, 19, 25 and 21
(iv) 3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9 and 7.6.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 28
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 29

Question 22.
Find the mean and the mode for the following data :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B Q22
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 30

Question 23.
Find the mode of:
(i) 5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 3
(ii) 7, 7, 8, 10, 10, 11, 10, 13, 14
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 31

Question 24.
Find the mode of :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B Q24
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 32

Question 25.
The heights (in cm) of 8 girls of a class are 140,142,135,133,137,150,148 and 138 respectively. Find the mean height of these girls and their median height.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 33

Question 26.
Find the mean, the median and the mode of:
(i) 12, 24, 24, 12, 30 and 12
(ii) 21, 24, 21, 6, 15, 18, 21, 45, 9, 6, 27 and 15.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 35

Question 27.
The following table shows the market positions of some brands of soap.
Draw a suitable bar graph :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B Q27
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 36

Question 28.
The birth rate per thousand of different countries over a particular period of time is shown below.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B Q28
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 21 Data Handling Ex 21B 37

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Mensuration Exercise 20A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The length and the breadth of a rectangular plot are 135 m and 65 m. Find, its perimeter and the cost of fencing it at the rate of ₹60 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 1

Question 2.
The length and breadth of a rectangular field are in the ratio 7 : 4. If its perimeter is 440 m, find its length and breadth. Also, find the cost of fencing it @ ₹150 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 2

Question 3.
The length of a rectangular field is 30 m and its diagonal is 34 m. Find the breadth of the field and its perimeter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 3

Question 4.
The diagonal of a square is 12\(\sqrt { 2 } \) cm. Find its perimeter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 4

Question 5.
Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 dm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 5

Question 6.
Find the perimeter of a rectangle with length = 24 cm and diagonal = 25 cm
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 6

Question 7.
The length and breadth of rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at the rate of ₹48 per metre is ₹19,200, find its length and breadth.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 7

Question 8.
A wire is in the shape of square of side 20 cm. If the wire is bent into a rectangle of length 24 cm, find its breadth.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 8

Question 9.
If P = perimeter of a rectangle, l= its length and b = its breadth find :
(i) P, if l = 38 cm and b = 27 cm
(ii) b, if P = 88 cm and l = 24 cm
(iii) l, if P = 96 m and b = 28 m
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 9
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 10

Question 10.
The cost of fencing a square field at the rate of
Cost of fencing 440 m = ₹150 x 440 = ₹75 per meter is
Cost of fencing 440 m = ₹150 x 440 = ₹67,500. Find the perimeter and the side of the square field.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 11

Question 11.
The length and the breadth of a rectangle are 36 cm and 28 cm. If its perimeter is equal to the perimeter of a square, find the side of the square.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 12

Question 12.
The radius of a circle is 21 cm. Find the circumference (Take π = 3 \(\frac { 1 }{ 7 }\) ).
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 13

Question 13.
The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = \(\frac { 22 }{ 7 }\)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 14

Question 14.
The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take n = \(\frac { 22 }{ 7 }\))
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 15

Question 15.
The radii of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π = \(\frac { 22 }{ 7 }\))
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 16

Question 16.
The diameter of a circle is 42 cm, find its perimeter. If the perimeter of the circle is doubled, what will be the radius of the new circle. (Take π = \(\frac { 22 }{ 7 }\) )
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 17

Question 17.
The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 18

Question 18.
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radii 15 cm and 8 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 19

Question 19.
Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm and 18 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 20

Question 20.
The circumference of a circle is eigth time the circumference of the circle with radius 12 cm. Find its diameter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 21

Question 21.
The radii of two circles are in the ratio 3 : 5, find the ratio between their circumferences.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 22

Question 22.
The circumferences of two circles are in the ratio 5 : 7, find the ratio between their radii.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 23

Question 23.
The perimeters of two squares are in the ratio 8:15, find the ratio between the lengths of their sides.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 24

Question 24.
The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 25

Question 25.
Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 26

Mensuration Exercise 20B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the area of a rectangle whose length and breadth are 25 cm and 16 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 27

Question 2.
The diagonal of a rectangular board is 1 m and its length is 96 cm. Find the area of the board.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 28

Question 3.
The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m2, find
(i) its perimeter
(ii) cost of fencing it at the rate of ₹40 per meter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 29

Question 4.
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 30

Question 5.
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m2.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 31

Question 6.
Find the area of the square whose perimeter is 56 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 32

Question 7.
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2 find the area of the lawn.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 33

Question 8.
For each figure, given below, find the area of shaded region : (All measurements are in cm)
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 35

Question 9.
One side of a parallelogram is 20 cm and its distance from the opposite side is 16 cm. Find the area of the parallelogram.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 36

Question 10.
The base of a parallelogram is thrice it height. If its area is 768 cm2, find the base and the height of the parallelogram.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 37

Question 11.
Find the area of the rhombus, if its diagonals are 30 cm and 24 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 38

Question 12.
If the area of a rhombus is 112 cm2 and one of its diagonals is 14 cm, find its other diagonal.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 39

Question 13.
One side of a parallelogram is 18 cm and its area is 153 cm2. Find the distance of the given side from its opposite side.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 40

Question 14.
The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 41

Question 15.
The area of a rhombus is 84 cm2 and its perimeter is 56 cm. Find its height.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 42

Question 16.
Find the area of a triangle whose base is 30 cm and height is 18 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 43

Question 17.
Find the height of a triangle whose base is 18 cm and area is 270 cm2.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 44

Question 18.
The area of a right-angled triangle is 160 cm2. If its one leg is 16 cm long, find the length of the other leg.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 45

Question 19.
Find the area of a right-angled triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 46
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 47

Question 20.
Find the area of an equilateral triangle whose each side is 16 cm. (Take \(\sqrt { 3 } \)= 1.73)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 48

Question 21.
The sides of a triangle are 21 cm, 17 cm and 10 cm. Find its area.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 49

Question 22.
Find the area of an isosceles triangle whose base is 16 cm and length of each of the equal sides is 10 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 50
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 51

Question 23.
Find the base of a triangle whose area is 360 cm2and height is 24 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 52

Question 24.
The legs of a right-angled triangle are in the ratio 4 :3 and its area is 4056 cm2. Find the length of its legs.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 53
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 54

Question 25.
The area of an equilateral triangle is (64 x \(\sqrt { 3 } \) ) cm2– Find the length of each side of the triangle.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 55

Question 26.
The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 56

Question 27.
The diameter of a circle is 20 cm. Taking π = 3.14, find the circumference and its area.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 57

Question 28.
The circumference of a circle exceeds its diameter by 18 cm. Find the radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 58

Question 29.
The ratio between the radii of two circles is 5 : 7. Find the ratio between their :
(i) circumference
(ii) areas
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 59
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 60

Question 30.
The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radii
(ii) diameters
(iii) circumference
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 61
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 62

Question 31.
A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 63

Question 32.
The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 64

Question 33.
The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheel.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 65

Question 34.
The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel one kilometre?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 66

Question 35.
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm2. Find the length of the wire. If the same wire is bent to a largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 67

Question 36.
A wire is along the boundary of a circle with radius 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 68

Question 37.
The length and the breadth of a rectangular paper are 35 cm and 22 cm. Find the area of the largest circle which can be cut out of this paper.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 69

Question 38.
From each comer of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B Q38
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 70

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency: Congruent Triangles

Congruency: Congruent Triangles Exercise 19 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, whether the pairs of triangles given in the following figures are congruent or not:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q1.1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 2

Question 2.
In the given figure, prove that:
∆ABD ≅ ∆ ACD
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 3

Question 3.
Prove that:
(i) ∆ABC ≡∆ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 4

Question 4.
Prove that:
(i) ∆ABD  ≡ ∆ACD
(ii) ∠B = ∠C
(iii) ∠ADB = ∠ADC
(iv) ∠ADB = 90°
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q4
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 5
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 6

Question 5.
In the given figure, prove that:
(i) ∆ACB ≅ ∆ECD
(ii) AB = ED
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q5
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 7

Question 6.
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 8

Question 7.
In the given figure, prove that: BD = BC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 9

Question 8.
In the given figure ;
∠1 = ∠2 and AB = AC. Prove that:
(i) ∠B = ∠C
(ii) BD = DC
(iii) AD is perpendicular to BC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 10

Question 9.
In the given figure prove tlyat:
(i) PQ = RS
(ii) PS = QR
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q9
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 11

Question 10.
(i) ∆ XYZ ≅ ∆ XPZ
(ii) YZ = PZ
(iii) ∠YXZ = ∠PXZ
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q10
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 12

Question 11.
In the given figure, prove that:
(i) ∆ABC ≅ ∆ DCB
(ii) AC=DB
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q11
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 13

Question 12.
In the given figure, prove that:
(i) ∆ AOD ≅ ∆ BOC
(ii) AD = BC
(iii) ∠ADB = ∠ACB
(iv) ∆ADB ≅ ∆BCA
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q12
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 14

Question 13.
ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that:
(i) AD = BE
(ii)BD = CE
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q13
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 15

Question 14.
Use the informations given in the following figure to prove triangles ABD and CBD are congruent.
Also, find the values of x and y.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q14
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 16
Question 15.
The given figure shows a triangle ABC in which AD is perpendicular to side BC and BD = CD. Prove that:
(i) ∆ABD ≅ ∆ACD
(ii) AB=AC
(iii) ∠B = ∠C
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles Q15
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 19 Congruency Congruent Triangles 17

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids (Representing 3-D in 2-D)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids (Representing 3-D in 2-D)

Recognition of solids Exercise 18 – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Identify the nets which can be used to form cubes
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 1

Question 2.
Draw at least three different nets for making cube.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 2

Question 3.
The figure, given below, shows shadows of some 3D objects, when seen under the lamp of an overhead projector :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids Q3
In each case, name the object.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 3

Question 4.
Using Euler’s formula, find the values of a, b, c and d.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids Q4
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 4

Question 5.
Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
Below are given two nets to make dice (cube), the numbers inserted in each square indicate the number of dots in it.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids Q5
Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 5

Question 6.
The following figures represent nets of some solids. Name the solids
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 6

Question 7.
Draw a map of your class room using proper scale and symbols for different objects.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 7

Question 8.
Draw a map of your school compound using proper scale and symbols for various features like play ground, main building, garden, etc.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 8

Question 9.
In the map of India, the distance between two cities is 13.8 cm.
Taking scale : 1 cm = 12 km, find the actual distance between these two cities.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 18 Recognition of Solids 9

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry (Including Reflection and Rotation)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry (Including Reflection and Rotation)

Symmetry Exercise 17A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
For each figure, given below, draw the line (s) of symmetry, if possible :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A Q1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A Q1.1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 1

Question 2.
Write capital letters A to Z of English alphabet ; and in each case, if possible, draw the largest number of lines of symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 2
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 3

Question 3.
By drawing a free hand sketch of each of the following, draw in each case, the line (s) of symmetry,
if any:
(i) a scalene triangle
(ii) an isosceles right angled triangle
(iii) a rhombus
(iv) a kite shaped figure triangle.
(v) a rectangle
(vi) a square
(vii) an isosceles
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 4

Question 4.
Draw a triangle with :
(i) no line of symmetry,
(ii) only one line of symmetry,
(iii) exactly two lines of symmetry,
(iv) exactly three lines of symmetry,
(v) more than three lines of symmetry.
In each case, if possible, represent the line/ lines of symmetry by dotted lines. Also, write the special name of the triangle drawn.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 5

Question 5.
Draw a quadrilateral with :
(i) no line of symmetry.
(ii) only one line of symmetry.
(iii) exactly two lines of symmetry.
(iv) exactly three lines of symmetry.
(v) exactly four lines of symmetry.
(vi) more than four lines of symmetry.
In each case, if possible, represent the line/ lines of symmetry by dotted lines. Also, write the special name of the quadrilateral drawn.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 6
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 7

Question 6.
Construct an equilateral triangle with each side 6 cm. In the triangle drawn, draw all the possible lines of symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 8

Question 7.
Construct a triangle ABC in which AB = AC = 5cin and BC = 5.6 cm. If possible, draw its lines of symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 9

Question 8.
Construct a triangle PQR such that PQ = QR = 5 .5 cm and angle PQR = 90°. If possible, draw its lines of symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 10
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 11

Question 9.
If possible, draw a rough sketch of a quadrilateral which has exactly two lines of symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 12

Question 10.
A quadrilateral ABCD is symmetric about its diagonal AC. Name tire sides of this quadrilateral which are equal.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17A 13

Symmetry Exercise 17B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
In each figure, given below, find the image of the point P in the line AB :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 14

Question 2.
In each figure, given below, find the image of the line segment AB in the line PQ :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 15

Question 3.
Complete the following table :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 16

Question 4.
A point P (7,3)|is reflected in x-axis to point P’. The point P’ is further reflected in v-axis to point P” Find :
(i) the co-ordinates of P’
(ii) the co-ordinates of P”
(iii) the image of P (7, 3) in origin.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 17

Question 5.
A point A (- 5, 4) is reflected in y-axis to point B. The point B is further reflected in origin to point C. find :
(i) the co-ordinates of B
(ii) the co-ordinates of C
(iii) the image of A (- 5, 4) in x-axis.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 18

Question 6.
The point P (3, – 8) is reflected in origin to point Q. The Point Q is further reflected in x-axis to point R. Find :
(i) the co-ordinates of Q
(ii) the co-ordinates of R
(iii) the image of P (3, – 8) in y-axis.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 19

Question 7.
Each of the points A (3, 0), B (7, 0), C (- 8, 0), D (- 7, 0) and E (0, 0) is reflected in x-axis to points A’, B’, C’, D’ and E’ respectively. Write the co-ordinates of each of the image points A’, B’, C’, D’ and E’.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 20

Question 8.
Each of the points A (0, 4), B (0, 10), C (0, – 4), D (0, – 6) and E (0, 0) is reflected in y-axis to points A’, B’, C’, D’ and E’ respectively. Write the co-ordinates of each of the image points A’, B’, C’, D’ and E’.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 21

Question 9.
Each of the points A (0, 7), B (8. 0), C (0, -5), D (- 7, 0) and E (0, 0) are reflected in origin to points A’, B’, C’, D’ and E’ respectively. Write the co-ordinates of each of the image points A’, B’, C’, D’ and E’.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 22

Question 10.
Mark points A (4, 5) and B (- 5, 4) on a graph paper. Find A’, the image of A in x-axis and B’, the image of B in x-axis.
Mark A’ and B’ also on the same graph paper.
(ii) Join AB and A’ B’ and
find if AB = A’ B’ ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 23

Question 11.
Mark points A (6, 4) and B (4, – 6) on a graph paper.
Find A’, the image of A in y-axis and B’, the image of B in y-axis. Mark A’ and B’ also on the same graph paper.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 24

Question 12.
Mark points A (- 6, 5) and B (- 4, – 6) on a graph paper. Find A’, the image of A in origin and B’, the image of B in origin. Mark A’ and B’ also on the same graph paper. Join AB and A’ B’. Is AB = A’ B’ ?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17B 25

Symmetry Exercise 17C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
How many lines of symmetry does a rhombus have?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 26
Question 2.
What is the order of rotational symmetry of a rhombus?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 27

Question 3.
Show that each of the following figures has two lines of symmetry and a rotational.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 28

Question 4.
Name a figure that has a line of symmetry but does not have any roational symmetry.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 29

Question 5.
In each of the following figures, draw all possible lines of symmetry and also write the order of rotational symmetry:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C Q5
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 30
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 17 Symmetry Ex 17C 31

Selina Concise Mathematics Class 7 ICSE Solutions