Question

A solid metallic cylinder is melted and formed into identical solid cones each having same radius and same height as that of the cylinder. The number of cones formed is:

Options

• 3

• 6

• 9

• 2

Answer 1

3

Explanation:

Given,

A solid metallic cylinder is melted and formed into identical solid cones.

Let no. of cones formed be n.

As, radius and height of cones formed is equal to the cylinder.

Let radius of cylinder and cone be r units, height of cylinder and cone be h units.

∴ Volume of cylinder = n × Volume of each cone

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

\[\Rightarrow n = \frac{3\pi r^2 h}{\pi r^2 h} = 3.\]