CBSE Class 8

RD Sharma Class 8 Solutions Chapter 27 Introduction to Graphs Ex 27.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 27 Introduction to Graphs Ex 27.1

Other Exercises

• RD Sharma Class 8 Solutions Chapter 27 Introduction to Graphs Ex 27.1
• RD Sharma Class 8 Solutions Chapter 27 Introduction to Graphs Ex 27.2

Question 1.
Plot the points (5,0 ), (5,1), (5, 8). Do they lie on a line ? What is your observation ?
Solution:
Draw XOX’ and YOY’ the co-ordinates axis on the graph.
Take 1 cm = 1 unit
Point A (5, 0), B (5, 1) and C (5, 8) have been plotted on the graph. By joining A, B and C, we see that these points lie on the same line which is 5 units from y-axis.

Question 2.
Plot the points (2, 8), (7, 8) and (12, 8). Join these points in pairs. Do they lie on a line ? What do you observe ?
Solution:
Draw XOX’ and YOY’, the co-ordinate axis on the graph.
Take 0.5 cm = 1 unit.
Now points A (2, 8), B (7, 8), and C (12, 8) have been plotted on the graph. By joining them, we see that these points lie on the same line which is at a distance of 8 unit from x-axis.

Question 3.
Locate the points :
(i) (1,1), (1,2), (1,3), (1,4)
(ii) (2,1), (2, 2), (2,3), (2,4)
(iii) (1,3), (2,3), (3,3), (4,3)
(iv) (1,4), (2,4), (3,4), (4,4).
Solution:
The points given in (i) and (ii) are locates in first graph.

(i) (1,1), (1,2), (1,3), (1,4)
(ii) (2,1), (2, 2), (2, 3), (2, 4)
Points of (iii) and (iv) are located in the adjoining graph.
(iii) (1, 3), (2, 3), (3, 3), (4, 3)
(iv) (1,4), (2, 4), (3, 4), (4,4)

Question 4.
Find the coordinates of points A, B, C, D in the figure

Solution:
Draw perpendicular from A, B, C and D on x-axis and also on y-axis.
A is 1 unit from y-axis and 1 unit from x-axis.
∴ Co-ordinates of A are (1,1)
B is 1 unit fr onr y-axis and 4 units from x-axis
∴ Co-ordinates of B are (1,4)
C is 4 units from y-axis and 6 units from x-axis
∴ Co-ordinates of C are (4, 6)
D is 5 units fromy-axis and 3 units from x-axis
∴ Co-ordinates of D are (5,3)

Question 5.
Find the coordinates of points P, Q, R and S in Fig.

Solution:
Through P, Q, R and S, draw perpendiculars on x-axis and also on y-axis.
(i) P is 10 units form >’-axis and 70 units from y-axis
∴ Co-ordinates of P are (10, 70)
(ii) Q is 12 unit from x-axis and 80 units from y-axis
∴ Co-ordinates of Q are (12, 80)
(iii) R is 16 units from x-axis and 100 units from y-axis
∴ Co-ordinates of R are (16, 100)
(iv) S is 20 units from x-axis and 120 units from y-axis
∴ Co-ordinates of S are (20, 120)

Question 6.
Write the coordinates of each of the vertices of each polygon in the figure.

Solution:
(i) In figure OXYZ
Co-ordinates of O are (0, 0) ∵It is the origin
Co-ordinates of X are (0, 2) ∵ It lies on y – axis
Co-ordinates of Y are (2, 2)
Co-ordinates of Z are (2, 0) ∵It lies on x-axis
(ii) In figure ABCD, draw perpendicular from A, B, C, D on x-axis and y-axis.
A is 4 unit from y-axis and 5 units from x- axis
∴ Co-ordinates of A are (4, 5)
B is 7 units from y-axis and 5 units from x – axis
∴ Co-ordinates of B are (7, 5)
C is 6 units from y-axis and 3 units from x- axis
∴ Co-ordinates of C are (6, 3)
D is 3 units from y-axis as well x-axis
∴ Co-ordinates of D are (3, 3)
(iii) In figure PQR, perpendiculars for P, Q, R are drawn on x-axis and also on y-axis.
∴ Co-ordinates of P are (7, 4), of Q are (9, 5) and of R are (9, 3).

Question 7.
Decide which of the following statements is true and which is false. Give reasons for your answer.
(i) A point whose x-coordinate is zero, will lie on they-axis.
(ii) A point whose y-coordinate is zero, will lie on x-axis.
(iii) The coordinates of the origin are (0, 0).
(iv) Points whose x and y coordinates are equal, lie on a line passing through the origin.
Solution:
(i) Correct: ∵ every point on y-axis, its x = 0
(ii) Correct: ∵ every point on x-axis, its y = 0
(iii) Correct
(iv) Correct

Hope given RD Sharma Class 8 Solutions Chapter 27 Introduction to Graphs Ex 27.1 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4

Other Exercises

• RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.1
• RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2
• RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.3
• RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4
• RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.5

Question 1.
Find the cube roots of each of the following integers :
(i) -125
(ii) -5832
(iii) -2744000
(iv) -753571
Solution:

Question 2.
Show that :

Solution:

Question 3.
Find the cube root of each of the following numbers :
(i) 8 x 125
(ii) -1728 x 216
(iii) -27 x 2744
(iv) -729 x -15625
Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Find the cube root of each of the following rational numbers.

Solution:

Question 6.
Find the cube root of each of the following rational numbers :
(i) 0.001728
(ii) 0.003375
(iii) 0.001
(iv) 1.331
Solution:

Question 7.
Evaluate each of the following :


Solution:

Question 8.
Show that :

Solution:

Question 9.
Fill in the Blanks :

Solution:

Question 10.
The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.
Solution:

Question 11.
Three numbers are to one another 2:3: 4. The sum of their cubes is 0.334125. Find the numbers.
Solution:

Question 12.
Find side of a cube whose volume is

Solution:

Question 13.
Evaluate :

Solution:

Question 14.
Find the cube root of the numbers : 2460375,20346417,210644875,57066625 using the fact that
(i) 2460375 = 3375 x 729
(i) 20346417 = 9261 x 2197
(iii) 210644875 = 42875 x 4913
(iv) 57066625 = 166375 x 343
Solution:

Question 15.
Find the units digit of the cube root of the following numbers ?
(i) 226981
(ii) 13824
(iii) 571787
(iv) 175616
Solution:
(i) 226981
In it unit digit is 1
∴The units digit of its cube root will be = 1
(∵ 1 x 1 x 1 = 1)
∴Tens digit of the cube root will be = 6
(ii) 13824
∵ The units digit of 13824 = 4
(∵ 4 X 4 X 4 = 64)
∴Units digit of the cube root of it = 4
(iii) 571787
∵ The units digit of 571787 is 7
∴The units digit of its cube root = 3
(∵ 3 x 3 x 3 = 27)
(iv) 175616
∵ The units digit of 175616 is 6
∴The units digit of its cube root = 6
(∵ 6 x 6 x 6=216)

Question 16.
Find the tens digit of the cube root of each of the numbers in Question No. 15.
Solution:
(i) In 226981
∵ Units digit is 1
∴Units digit of its cube root = 1
We have 226
(Leaving three digits number 981)
6³ = 216 and 7³ = 343
∴6³ ∠226 ∠ T
∴The ten’s digit of cube root will be 6
(ii) In 13824
Leaving three digits number 824, we have 13
∵ (2)³ = 8, (3)³ = 27
∴2³ ∠13 ∠3′
∴Tens digit of cube root will be 2
(iii) In 571787
Leaving three digits number 787, we have 571
8³ = 512, 9³ = 729
∴ 8³ ∠571 ∠9³
Tens digit of the cube root will be = 8
(iv) In 175616
Leaving three digit number 616, we have 175
∵ 5³ = 125, 6³ = 216
∴5³ ∠175 ∠6³
∴Tens digit of the cube root will be = 5

Hope given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.