Question

If the volumes of two cones are in the ratio of 1 : 4 and their diameters are in the ratio of 4 : 5, the ratio of their heights is

• A. 25:64
• B. 64:25
• C. 16:36

Answer 1

The correct option is A 25:64

Here, $\frac{d_1}{d_2}=\frac{4}{5}$

$\Rightarrow \frac{r_1}{r_2}=\frac{4}{5}$

Now, $\frac{V_1}{V_2}=\frac{\frac{1}{3}\pi r_1^2{h}_1}{\frac{1}{3}\pi r_2^2{h}_2}=\frac{r_1^2{h}_1}{r_2^2{h}_2}$

$\Rightarrow \frac{V_1}{V_2}=\frac{r_1^2}{r_2^2}\times \frac{h_1}{h_2}$

$\Rightarrow \frac{1}{4}={\left(\frac{4}{5}\right)}^2\times \frac{h_1}{h_2}$

$\Rightarrow \frac{h_1}{h_2}=\frac{25}{64}$