Question

A cone and a sphere have equal volumes. Their radii are also equal each being 10 cm; the height of the cone is:

विकल्प

• 70 cm

• 40 cm

• 50 cm

• 20 cm

Answer 1

40 cm

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

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

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

\[\Rightarrow h = 4r\]

\[\Rightarrow h = 4 \times 10 = 40\ \text{cm}.\]