Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

Options

• 12 cm

• 14 cm

• 15 cm

• 18 cm

Answer 1

External radius `r_1 = 8/2 = 4 cm`

Internal radius `r_2 = 4/2 = 2cm`

The volume of hollow sphere

\[V = \frac{4}{3}\pi\left( R^3 - r^3 \right)\]

\[ = \frac{4}{3}\pi\left( 4^3 - 2^3 \right)\]

Let h be the height of cone.

Clearly,

The volume of recasted cone = volume of hollow sphere

\[\frac{1}{3} \pi r^2 h = \frac{4}{3}\pi\left( 4^3 - 2^3 \right)\]

\[ \Rightarrow 4^2 h = 4\left( 4^3 - 2^3 \right)\]

\[ \Rightarrow h = 14 cm\]

Hence, the height of cone = 14 cm