Question

Two cones $A$ and $B$ have their base radii in the ratio of $4:3$ and their heights in the ratio $3:4$. The ratio of volume of cone $A$ to that of cone $B$ is

• A. $4:3$
• B. $3:4$
• C. $2:3$
• D. $1:2$

Answer 1

The correct option is A $4:3$

Let the base radii of two cones $A$ and $B$ be $r_1$ and $r_2$

and heights be $h_1$ and $h_2$.

Given, $\frac{r_1}{r_2}=4:3$
and $\frac{h_1}{h_2}=3:4$
Volume of a cone $=$ $\frac{1}{3}\pi r^{2}h$
$\therefore \frac{V_A}{V_B}=\frac{\frac{1}{3}\pi (r_1{)}^2{h}_1}{\frac{1}{3}\pi (r_2{)}^2{h}_2}$
$=$ ${\left(\frac{4}{3}\right)}^2\times \frac{3}{4}$
$=$ $\frac{4}{3}$