Question

(a) The areas of two circles are in the ratio $4:9$. Find the ratio of their circumferences.
(b) The circumference of two circles is in the ratio $3:4$. Find the ratio of their areas.

Answer 1

a) Area of two circles in ratio $=4:9$

${\pi r}_1^2:{\pi r}_2^2=4:9$

$\frac{r_1^2}{r_2^2}=\frac{4}{9}$

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

Circumference $=2\pi r_1:{2\pi r}_2=\frac{2\pi \times 2}{2\pi \times 3}=2:3$

Answer = $2:3$

b)Circumference of circle ratios $=3:4$

$⟹\frac{r_1}{r_2}=\frac{3}{4}$

Area of circles $=\frac{{\pi r}_1^2}{{\pi r}_2^2}=\frac{r_1^2}{r_2^2}$$=\frac{3^2}{4^2}=\frac{9}{16}=9:16$

Answer = $9:16$