Question

The ratio of the radii of two circles is $4:5$. Find the ratio of their areas.

Answer 1

$A_1=2\pi r_1^2$ $4r_1=5r_2$

$\frac{A_1}{r_1^2}=2\pi =\frac{A_2}{r_2^2}$ $r_1=\frac{5r_2}{4}$

$\frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}=\frac{(\frac{5r_2}{4}{)}^2}{r_2^2}=\frac{5^2}{4^2}$

$16A_1=25A_2$ $\therefore 16:25$