Question

If the radii of a cone and a cylinder are in the ratio 2 : 3 ad their heights are in the ratio 4 : 3 then the ratio of their volumes will be

• A. 16 : 27
• B. 16 : 81
• C. 16 : 9
• D. 27 : 16

Answer 1

The correct option is B 16 : 81

$\frac{r_1}{r_2}=\frac{2}{3},\frac{h_1}{h_2}=\frac{4}{3}$

$\frac{V_{cone}}{V_{cylinder}}=\frac{\frac{1}{3}\pi r_1^2{h}_1}{\pi r_2^2{h}_2}=\frac{1}{3}\times (\frac{r_1}{r_2}{)}^2\times (\frac{h_1}{h_2})$

$=\frac{1}{3}\times \frac{4}{9}\times \frac{4}{3}$

$=\frac{16}{81}$

So ratio =16 : 81