Draw a graph for the radius and circumference of circle using a suitable scale.
(Hint : Take radius = 7, 14, 21 units and so on)
From the graph,
(a) Find the circumference of the circle when radius is 42 units.
(b) At what radius will the circumference of the circle be 220 units?

Solution:

The table below gives the circumference of the circle for various radii of the circle:

The graph of the table is drawn below:

(a) From the graph the circumference of the circle can be found out when the radius ‘r’ is 42 as follows:

From point 42 on the x-axis(horizontal axis) we draw a straight line to the point B on the straight line graph OA. From point B we draw a horizontal line to the vertical axis i.e. y-axis. The horizontal line meets the vertical axis at the point marked 244. Hence the circumference of the circle when r = 42 is 244

(b) Similarly to find the radius of the circle when the circumference is 220 we have to draw a horizontal line from the point 220 on the y-axis(vertical axis) to the point C on the straight line graph OA. From point C we drop a vertical line onto the x-axis(horizontal axis) and we find that the vertical line touches the x-axis at point 35. Therefore the radius is 35 when the circumference is 220.

✦ Try This: Draw a graph for the side of the square and the perimeter of the square using a suitable scale.

(Hint : Assume the length of the side of the square and its perimeter will be four times the side of the square)

Using the graph find:

(a) The perimeter if the side of the square is 5

(b) The side of the square if the perimeter is 36

The graph can drawn with the help of the following table:
 

(a) To find the perimeter when the side of the square is given as s = 5 the following needs to be done. Draw a vertical line from point (5) on the x-axis(horizontal axis) to the straight line graph AB at point D. From point D we draw a horizontal line to the vertical axis(y-axis) at point 20 . Therefore the perimeter of the square when the side is 5 is 20.

(b) To find the side of the square when the perimeter is given can be found out in the following way - Draw a horizontal line from point 36 on the vertical axis(y-axis) to the line graph AB at point C. From point C a vertical line is dropped on the x-axis(horizontal axis) and the point obtained is 9 on the x-axis. Therefore, if the perimeter then the side of the square is 9

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 15

NCERT Exemplar Class 8 Maths Chapter 12 Problem 50

Draw a graph for the radius and circumference of circle using a suitable scale. From the graph, (a) Find the circumference of the circle when radius is 42 units, (b) At what radius will the circumference of the circle be 220 units?

Summary:

The graph of the table giving the circumference(C) of the circle for different radii has been plotted in the solution above. when ‘r’ is 42, C is 144, and when C = 220 radius is 35.

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