Question

The circumferences of two circles are in the ratio 2 : 3. What is the ratio between their areas?

Answer 1

Ratio of circumference=2:3

Circumference of first circle = 2$\pi$$r_1$

Circumference of second circle = 2$\pi$$r_2$

As per question;

$\frac{Circumferenceoffirstcircle}{Circumferenceofsecondcircle}$ = $\frac{2}{3}$

$\frac{2\pi r_1}{2\pi r_2}$ = $\frac{2}{3}$

$\frac{r_1}{r_2}$ = $\frac{2}{3}$

Area of first circle = $\pi$$r_1^2$

Area of second circle = $\pi$$r_2^2$

Ratio of area of first circle toarea of first circle = $\frac{r_1^2}{r_2^2}$

=$\frac{4}{9}$