Question

A cylindrical bucket, 32 cm high and with radius of base 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

Height (h₁) of cylindrical bucket = 32 cm

Radius (r₁) of circular end of bucket = 18 cm

Height (h₂) of conical heap = 24 cm

Let the radius of the circular end of conical heap be r₂.

The volume of sand in the cylindrical bucket will be equal to the volume of sand in the conical heap.

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

r₂ = 18 x 2=36 cm

Slant height = 

Therefore, the radius and slant height of the conical heap are 36 cm and 12√13 cm respectively