Question

A cylindrical vessel 32 cm high and 18 cm as the radius of the base, 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, the radius of its base is

Options

• 12 cm

•  24 cm

• 36 cm

•  48 cm

Answer 1

Volume of sand filled in cylindrical vessel

`= pi(18)^2 xx 32`

`= 32 xx 324 pi`

Clearly,

The volume of conical heap = volume of sand

`1/3 pir^2 xx 24 = 32 xx 324 pi`

                 `r^2 = (32 xx 324)/8`

                   `r = sqrt(4 xx 324)`

                   `r = 2 xx 18`

                     `= 36`

                   `r = 36 cm`