Question

The circumferences of two circles are in the ratio 3 : 4. The ratio of their area is

(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9

Answer 1

Let the radius of both circles are a, b respectively.

The circumference of the circle = 2$\pi$r

Given the circumferences of two circles are in the ratio 3 : 4.

$\frac{2\pi a}{2\pi b}=\frac{3}{4}$

$\frac{a}{b}=\frac{3}{4}$

Area of circle = $\pi \times r^2$

The ratio of their areas = $\frac{\pi \times a^2}{\pi \times b^2}=(\frac{a}{b}{)}^2=(\frac{3}{4}{)}^2=\frac{9}{16}$
The ratio of their area is 9:16 (c)