Question

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

• A. $34:25$
• B. $24:55$
• C. $44:25$
• D. $24:25$

Answer 1

The correct option is D $24:25$

volume of cone $\propto \left(radius{)}^2\right(height)$

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

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

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

Ratio of height $=25:64R$