Question

A cone of height 30 cm is melted and recast into a cylinder of the same base. Find the height of the cylinder.

Answer 1

Given:

 A right circular cone of height 30 cm is melted and recast into a cylinder having the same base (same radius r). This is a standard volume-conservation problem.

Let the common base radius = r and the required height of the cylinder = H cm.

Volume of cone = `(1/3)πr^2 × 30 = 10πr^2`.

Volume of cylinder = `πr^2 xx H.`

Equate volumes (material conserved): `πr^2 H = 10πr^2.`

Cancel `πr^2 (r ≠ 0): H`

= 10.