Question

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

Answer 1

Given, radius of the base of the bucket = 18 cm

Height of the bucket = 32 cm ‘

So, volume of the sand in cylindrical bucket = πr²h= π (18)² x 32 = 10368 π

Also, given height of the conical heap (h) = 24 cm

Let radius of heap be r cm.

According to the question,

Volume of the sand in cylindrical bucket = Volume of the sand in conical heap

Hence, radius of conical heap of sand = 36 cm

and slant height of conical heap = 43.267 cm