Question

A sphere and a cone have equal volumes and equal radii. The ratio between the radius and height of the cone is:

Options

• 3 : 4

• 4 : 3

• 4 : 1

• 1 : 4

Answer 1

1 : 4

Explanation:

Let radius of cone and sphere be r cm and height of cone be h cm.

Given,

A cone and a sphere have equal volumes and their radius are equal.

∴ Volume of cone = Volume of sphere

\[\Rightarrow \frac{1}{3}\, \pi r^2 h = \frac{4}{3}\, \pi r^3\]

\[\Rightarrow h = \frac{4 \times 3\pi r^3}{3\pi r^2}\]

\[\Rightarrow h = 4r\]

\[\Rightarrow \frac{r}{h} = \frac{1}{4}\]

\[\Rightarrow r : h = 1 : 4.\]