Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

Options

•  13 : 22

• 14 : 11

•  22 : 13

• 11 : 14

Answer 1

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

Explanation:

Let radius of circle be r and side of a square be a.

Perimeter of a circle = Perimeter of a square

∴ `2pir = 4a`

⇒ `a = (pir)/2`  .....(i)

Now, `"Area of circle"/"Area of square" = (pir^2)/(a)^2 = pi^2/((pir/2)^2`  ......[From equation (i)]

= `(pir^2)/((pi^2r^2)/4) = 4/pi`

= `4/(22/7) = 28/22`

= `14/11`