Question

Volume of two spheres are in ratio 64: 27. Find the ratio of their surface areas.

Answer 1

Volume of S1/ Volume of S2 = $\frac{64}{27}$

$\frac{\left(\frac{4}{3}\pi r^3\right)}{\left(\frac{4}{3}\pi r^3\right)}=\frac{64}{27}{\left(\frac{r}{R}\right)}^3=\frac{64}{27}\frac{r}{R}=\frac{4}{3}$

Surface area of $s1$/ surface area of $s2=\frac{4\pi r^2}{4\pi r^2}=\frac{16}{9}$