Question

Two solid cones $A$ and $B$ are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is $2:1$. Find their heights.

• A. $14$cm, $14$cm
• B. $15$cm, $6$cm
• C. $14$cm, $7$cm
• D. $10$cm, $11$cm

Answer 1

The correct option is C $14$cm, $7$cm

The ratio of volume of cones $A$ and $B$ is $2:1$, that is:

$\frac{V_A}{V_B}=\frac{2}{1}$

Let the height of the cone $A$ be $h$ then the height of the cone $A$ will be $(21-h)$.

$\frac{V_A}{V_B}=\frac{2}{1}\Rightarrow \frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^2(21-h)}=\frac{2}{1}\Rightarrow \frac{h}{21-h}=\frac{2}{1}\Rightarrow h=42-2h\Rightarrow 3h=42\Rightarrow h=14$

Since the height of cone $A$ is $14$ cm, therefore, the height of cone $B$ is $21-14=7$ cm.

Hence, the heights are $14$ cm and $7$ cm.