Question

A cylindrical vessel 32 cm high and 18 cm radius is filled with sand. This is emptied on the ground and a conical heap of sand is formed. If the height of the heap is 24 cm, find the radius of its base.

Answer 1

Given:

Cylinder: height = 32 cm, radius = 18 cm.

Cone (heap): height = 24 cm, base radius = r (to find).

Volume of cylinder = π × (18)² × 32 = 10368 π cm³

Volume of cone = `(1/3)` π r² × 24

= 8 π r² cm3

Sand volume is conserved, so equate volumes: 8 πr²

= 10368 π

r² = `10368/8`   ...[Cancel π and solve]

= 1296

⇒ r = `sqrt1296`

= 36 cm