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 of cylindrical bucket, h = 32 cm. 

Radius, r = 18 cm.

Height of conical heap of sand = 24 cm. 

Radius, r = ? 

Slant height, l = ? 

Volume of conical heap of sand = Volume of Cylinder.

Radius of Cone, r = 36 cm. 

Slant height of cone,

∴ Radius of cone, r = 36 cm. 

Slant height of cone, h = 12√13 cm