Question

The ratio of radius of two sphere is $3:2$. Find the ratio of the surface area and volume.

Answer 1

Given that,

$r_1:r_2=2:3$

We know that,

Surface area $=4\pi r^2$

$\frac{4\pi {r_1}^2}{4\pi {r_2}^2}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{3}{2}\right)}^2=9:4$

We know that,

Volume area $=\frac{4}{3}\pi r^3$

$\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi {r_2}^3}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{3}{2}\right)}^3=27:8$

Hence,

We get Surface area ratio$=9:4$ and

Volume ratio$=27:8$