If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
a. 22:7
b. 14:11
c. 7:22
d. 11:14

Solution:

Given, the perimeter of a circle is equal to that of a square.

We have to find the ratio of their areas.

Perimeter of circle = circumference.

Circumference of circle = 2πr

Where, r is the radius

Perimeter of square = 4a

Where a is the side length

Given, 2πr = 4a

r/a = 4/2π

r/a = 2/π ------------ (1)

Area of circle = πr²

Area of square = a²

Now, area of circle/area of square = πr²/a²

Substitute (1) in the above expression,

= π(2/π)²

= 4/π

= 4(7)/22

= 28/22

= 14/11

Therefore, the ratio of the area of circle to the area of square is 14:11

✦ Try This: If the perimeter of square is 44 cm, find the area of the circle whose circumference is equal to the perimeter of square.

Given, perimeter of square = 44 cm

Perimeter of square = circumference of circle

We have to find the area of the circle.

Circumference of circle = 2πr

44 = 2(22/7)r

44 = 44r/7

r = 7 cm

Area of the circle = πr²

= (22/7)(49)

= 22(7)

= 154 square cm.

Therefore, the area of the circle is 154 square cm.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

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NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 5

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is a. 22:7, b. 14:11, c. 7:22, d. 11:14

Summary:

The perimeter of a circle is its boundary or the complete arc length of the periphery of a circle. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14:11

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☛ Related Questions:

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