Volumes Practice Test 3

In the first case :
2πr = 30
r = $\frac{15}{\mathit{\pi }}$ cm and h = 20 cm
⇒ Volume $\left({\mathit{V}}_1\right)$ = $\mathit{\pi }{\mathit{r}}^2\mathit{h}$ = $\frac{15\times 15\times 20}{\mathit{\pi }}$ = $\frac{4500}{\mathit{\pi }}$ cu cm
In the second case :
2πr = 20 ⇒ r = $\frac{10}{\mathit{\pi }}$ cm and h = 30 cm
∴ Volume $\left({\mathit{V}}_2\right)$ = $\mathit{\pi }{\mathit{r}}^2\mathit{h}$ = $\frac{10\times 10\times 30}{\mathit{\pi }}$ = $\frac{3000}{\mathit{\pi }}$ cu cm
Hence, ratio of the two volumes = ${\mathit{V}}_1:{\mathit{V}}_2$ = $\frac{4500}{\mathit{\pi }}:\frac{3000}{\mathit{\pi }}$ = 3 : 2