Two tables, A and B are given below. Draw graphs for quantities shown in the tables and find out whether Y 2 - Y 1 X 2 - X 1 is constant? Table A X 1 X 2 X 3 X 4 X 5 Radius of a circle, r in cm 2 4 6 8 10 Perimeter of a circle, 2 πr in cm 4 π 8 π 12 π 16 π 20 π Y 1 Y 2 Y 3 Y 4 Y 5 Table B X 1 X 2 X 3 X 4 X 5 Radius of a circle, r in cm 1 2 3 4 5 Area of a circle, A = πr 2 in cm 2 π 4 π 9 π 16 π 25 π Y 1 Y 2 Y 3 Y 4 Y 5

First, we shall draw the graph for quantities shown in the table A . Table A X 1 X 2 X 3 X 4 X 5 Radius of a circle, r in cm 2 4 6 8 10 Perimeter of a circle, 2 πr in cm 4 π 8 π 12 π 16 π 20 π Y 1 Y 2 Y 3 Y 4 Y 5 Here, the radius in cm will be considered as the independent variables X and these will be represented on the X -axis. The perimeter of the circle (in cm ) are considered the dependent variables Y and these will be represented on the Y -axis. The scale chosen on the X -axis is: 1 unit = 1 cm and, the scale chosen on the Y -axis is: 1 unit = 2 π cm . Now, we plot the points X 1 , Y 1 = 2 , 4 π , X 2 , Y 2 = ( 4 , 8 π ) , X 3 , Y 3 = ( 6 , 12 π ) , X 4 , Y 4 = ( 8 , 16 π ) and X 5 , Y 5 = ( 10 , 20 π ) on the graph paper and draw a line connecting the points. The line is the required graph as shown below. Now, for this graph of table A , Y 2 - Y 1 X 2 - X 1 = 8 π - 4 π 4 - 2 = 4 π 2 = 2 π . -----(i) Now, we shall draw the graph for quantities shown in the table B . Table B X 1 X 2 X 3 X 4 X 5 Radius of a circle, r in cm 1 2 3 4 5 Area of a circle, A = πr 2 in cm 2 π 4 π 9 π 16 π 25 π Y 1 Y 2 Y 3 Y 4 Y 5 Here, the radius in cm will be considered as the independent variables X and these will be represented in the X -axis. The area of the circle ( πr 2 in cm 2 ) is considered the dependent variables Y and these will be represented in the Y -axis. The scale chosen on the X -axis is: 2 units = 1 cm and, the scale chosen on the Y -axis is: 2 units = 5 π cm 2 . Now, we plot the points X 1 , Y 1 = 1 , π , X 2 , Y 2 = ( 2 , 4 π ) , X 3 , Y 3 = ( 3 , 9 π ) , X 4 , Y 4 = ( 4 , 16 π ) and X 5 , Y 5 = ( 5 , 25 π ) on the graph paper and draw a line connecting the points. The line is the required graph of table B as shown below. Note that the graph is a curved parabolic line. Now, for this graph of table B , Y 2 - Y 1 X 2 - X 1 = 4 π - π 2 - 1 = 3 π 1 = 3 π . -----(ii) From (i) and (ii), we get, 2 π ≠ 3 π . Therefore, Y 2 - Y 1 X 2 - X 1 is not constant for the two graphs A and B .

MEDIUM

10th Chhattisgarh Board

IMPORTANT

Earn 100

Anita made some musical instruments using pipes of different lengths. The mathematical relation between the length of pipe (in $cm$ ) and the pitch (cycles per second) of music is shown in the table below:

Pitch (cycles per second) $64$ $128$ $192$ $261$ $300$ $395$ $438$ $512$

Length of pipe (in $cm$ ) $80$ $41$ $26$ $19$ $18$ $13$ $12$ $10$

Look at the graph and answer the following question:
What should be the length of pipe to obtain a pitch of $160$ cycles per second?

Important Questions on Graphs

MEDIUM

10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 7 - Graphs>Exercise–1>Q 7

Anita made some musical instruments using pipes of different lengths. The mathematical relation between the length of pipe (in $cm$ ) and the pitch (cycles per second) of music is shown in the table below:

Pitch (cycles per second)	$64$	$128$	$192$	$261$	$300$	$395$	$438$	$512$
Length of pipe (in $cm$ )	$80$	$41$	$26$	$19$	$18$	$13$	$12$	$10$

Question Image

Look at the graph and answer the following questions:
What will be the pitch when the length of pipe is $60 cm ?$

HARD

10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 7 - Graphs>Exercise–1>Q 8

Two tables, $A$ and $B$ are given below. Draw graphs for quantities shown in the tables and find out whether $\frac{Y_{2} - Y_{1}}{X_{2} - X_{1}}$ is constant?

Table $A$
	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
Radius of a circle, $r$ in $cm$	$2$	$4$	$6$	$8$	$10$
Perimeter of a circle, $2 πr$ in $cm$	$4 π$	$8 π$	$12 π$	$16 π$	$20 π$
	$Y_{1}$	$Y_{2}$	$Y_{3}$	$Y_{4}$	$Y_{5}$

Table $B$
	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
Radius of a circle, $r$ in $cm$	$1$	$2$	$3$	$4$	$5$
Area of a circle, $A = {πr}^{2}$ in ${cm}^{2}$	$π$	$4 π$	$9 π$	$16 π$	$25 π$
	$Y_{1}$	$Y_{2}$	$Y_{3}$	$Y_{4}$	$Y_{5}$