Surface Areas and Volumes — Maths STD 9 — Question

Solution:

Let radius of hemisphere is r.

Volume of a cone, $\text{V}_1=\frac{1}{3}\pi\text{r}^2\text{h}$

$\text{V}_1=\frac{1}{3}\pi\text{r}^2(\text{r})\ \ [\therefore\text{h=r}]$

$=\frac{1}{3}\pi\text{r}^3$

Volume of a hemisphere, $\text{V}_2=\frac{2}{3}\pi\text{r}^3$

Volume of cylinder, $\text{V}_3=\pi\text{r}^2\text{h}=\pi\text{r}^2\times\text{r}=\pi\text{r}^3\ \ [\therefore\text{h}=\text{r}]$

$\text{V}_1:\text{V}_2:\text{V}_3=\frac{1}{2}\pi\text{r}^3:\frac{2}{3}\pi\text{r}^3=1:2:3$

Hence, the ratio of their volumes is 1 : 2 : 3.