RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b

RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b.

Other Exercises

Question 1.
Solution:
Circumference of circle = 2πr = 39.6 cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 1

Question 2.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 2

Question 3.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 3

Question 4.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 4

Question 5.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 5

Question 6.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 6

Question 7.
Solution:
Let the radii of circles be x cm and (7 – x) cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 7
Circumference of the circles are 26 cm and 18 cm.

Question 8.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 8

Question 9.
Solution:
Inner radius of the circular park = 17 m
Width of the path = 8 m
Outer radius of the circular park = (17 + 8)m = 25 m
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 9

Question 10.
Solution:
Let r m and R m be the radii of inner circle and outer boundaries respectively.
Then, 2πr = 352 and 2πR = 396
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 10

Question 11.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 11

Question 12.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 12

Question 13.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 13

Question 14.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 14

Question 15.
Solution:
∆OAB is equilateral.
So, ∠AOB = 60
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 15

Question 16.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 16
Area of minor segment = (area of sector OACBO) – (area of ∆OAB)
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 17

Question 17.
Solution:
Area of sector OACBO
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 18

Question 18.
Solution:
Let AB be the chord of circle of centre O and radius = 30 cm such that ∠AOB = 600
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 19
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 20

Question 19.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 21

Question 20.
Solution:
In 2 days, the short hand will complete 4 rounds
Distance travelled by its tip in 2 days
=4(circumference of the circle with r = 4 cm)
= (4 × 2π × 4) cm = 32π cm
In 2 days, the long hand will complete 48 rounds length moved by its tip
= 48(circumference of the circle with r = 6cm)
= (48 × 2π × 6) cm = 576π cm
Sum of the lengths moved
= (32π + 576π) = 608π cm
= (608 × 3.14) cm = 1909.12 cm

Question 21.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 22

Question 22.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 23

Question 23.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 24

Question 24.
Solution:
Each angle of equilateral triangle is 600
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 25
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 26
Area that the horse cannot graze is 36.68 m2

Question 25.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 27

Question 26.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 28
OP = OR = OQ = r
Let OQ and PR intersect at S
We know the diagonals of a rhombus bisect each other at right angle.
Therefore we have
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 29

Question 27.
Solution:
Diameter of the inscribed circle = Side of the square = 10 cm
Radius of the inscribed circle = 5 cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 30
Diameter of the circumscribed circle
= Diagonal of the square
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 31

Question 28.
Solution:
Let the radius of circle be r cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 32
Then diagonal of square = diameter of circle = 2r cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 33

Question 29.
Solution:
Let the radius of circle be r cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 34
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 35

Question 30.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 36

Question 31.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 37

Question 32.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 38

Question 33.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 39

Question 34.
Solution:
Distance covered by a wheel in 1minute
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 40

Question 35.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 41

Question 36.
Solution:
Each side of the square is 14 cm
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 42

Question 37.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 43
Let A, B, C, D be the centres of these circles
Join AB, BC, CD and DA
Side of square = 10 cm
Area of square ABCD
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 44

Question 38.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 45
Required area = [area of square – areas of quadrants of circles]
Let the side = 2a unit and radius = a units
Area of square = (side × side) = (2a × 2a) sq. units
= 4a2sq. units
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 46

Question 39.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 47
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 48

Question 40.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 49
Let A, B, C be the centers of these circles. Join AB, BC, CA
Required area= (area of ∆ABC with each side 2) -3[area of sector with r = a cm, θ= 600]
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 50

Question 41.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 51

Question 42.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 52

Question 43.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 53

Question 44.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 54

Question 45.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 55

Question 46.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 56

Question 47.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 57

Question 48.
Solution
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 58

Question 49.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 59

Question 50.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 60

Question 51.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 61
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 62

Question 52.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 63
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 64

Question 53.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 64
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 66

Question 54.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 67

Question 55.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 68

Question 56.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 69

Question 57.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 70

Question 58.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 71
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 72

Question 59.
Solution:
PS = 12 cm
PQ = QR = RS = 4 cm, QS = 8 cm
Perimeter = arc PTS + arc PBQ + arc QES
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 73

Question 60.
Solution:
RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment Ex 18b 74

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