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If the circumference of a circle and the perimeter of a square are equal, then
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square

Solution:

Given, the circumference of a circle and the perimeter of a square are equal.

We have to find the relation between the areas of the circle and square.

Circumference of circle = 2πr

Where, r is the radius

Where a is the side length

Given, 2πr = 4a

πr = 2a

(22/7)r = 2a

r = (2a)(7/22)

r = a(7/11)

r = 7a/11

Also, a = 11r/7

= (22/7)(7a/11)²

= (22/7)(49a²/121)

= (2/7)(49a²/11)

= (2)(7a²/11)

A₁ = 14a²/11

So, A₁ = (14/11)A₂

This implies A₁ > A₂

Therefore, area of circle > area of square.

✦ Try This: The radius of a circle whose circumference is equal to 110 cm is

Given, circumference of circle is 110 cm

We have to find the radius of the circle.

Circumference of circle = 2πr

110 = 2(22/7)r

110 = 44r/7

r = 110(7)/44

r = 5(7)/2

r = 35/2

r = 17.5 cm

Therefore, the radius of circle is 17.5 cm

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

NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 3

If the circumference of a circle and the perimeter of a square are equal, then (A) Area of the circle = Area of the square, (B) Area of the circle > Area of the square, (C) Area of the circle < Area of the square, (D) Nothing definite can be said about the relation between the areas of the circle and square

Summary:

If the circumference of a circle and the perimeter of a square are equal, then area of circle > area of square

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