Question

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is

(a) 4 : $\pi$ (b) $\pi$ : 4 (c) $\pi$ : 7 (d) 7 : $\pi$

Answer 1

Circumference = perimeter

$2\pi r=4a$

$r=\frac{2a}{\pi }$

$\frac{\text{Area of the square}}{\text{Area of circle}}=\frac{a^2}{\pi r^2}$

$=\frac{a^2}{\pi \times \frac{2a}{\pi }\times \frac{2a}{\pi }}$

$=\frac{\pi a^2}{4a^2}=\frac{\pi }{4}=\pi :4$