Question

A cone and a sphere have equal volumes. If height of the cone = radius of the sphere =10 cm, the radius of the cone is:

Options

• 40 cm

• 10 cm

• 30 cm

• 20 cm

Answer 1

20 cm

Explanation:

Given,

Height of the cone (H) = radius of the sphere (r) = 10 cm

Volume of cone and sphere are equal.

Let radius of cone be R cm.

\[\therefore \frac{1}{3}\, \pi R^2 H = \frac{4}{3}\, \pi r^3\]

\[\Rightarrow R^2 H = 4r^3\]

\[\Rightarrow R^2 = \frac{4r^3}{H}\]

\[\Rightarrow R^2 = \frac{4 \times 10^3}{10}\]

\[\Rightarrow R^2 = 4 \times 10^2\]

\[\Rightarrow R^2 = 400\]

\[\Rightarrow R = \sqrt{400} = 20\ \text{cm}.\]