Question

If the circumference of a circle and the perimeter of a square are equal, then ______.

Options

• Area of the circle = Area of the square

• Area of the circle  < Area of the  square

• Area of the circle > Area of the square

• Nothing definite can be said about the relation between the areas of the circle and square.

Answer 1

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

Explanation:

Circumference of a circle = Perimeter of square

`2pir = 4a`  .....[Where r and a are radius of circle and side of square respectively]

⇒ `22/7 r = 2a`

⇒ `11r = 7a`

⇒ `a = 11/7 r`

⇒ `r = (7a)/11`  ......(i)

Now, Area of circle, `A_1 = pir^2`

= `pi((7a)/11)^2 = 22/7 xx (49a^2)/121`  .....[From equation (i)]

= `(14a^2)/11`  ......(ii)

And Area of square, `A_2 = (a)^2`  .....(iii)

From equations (ii) and (iii), `A_1 - 14/11 A_2`

∴ `A_1 > A_2`

Hence, Area of the circle > Area of the square.