#### 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.

#### Solution

Height (*h*_{1}) of cylindrical bucket = 32 cm

Radius (*r*_{1}) of circular end of bucket = 18 cm

Height (*h*_{2}) of conical heap = 24 cm

Let the radius of the circular end of conical heap be *r*_{2.}

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

`pixxr_1^2xxh_1=1/3pixxr_2^2xxh_2`

`pixx18^2xx32=1/3pixxr_2^2xx24`

`pixx18^2xx32= 1.3pixxr_2^2xx24`

`r_2^2= (3xx18^2xx32)/24 = 18^2 xx 4`

r_{2} = 18 x 2 = 36 cm

Slant height = `sqrt(36^2+24^2) = sqrt(12^2xx(3^2+2^2)) = 12sqrt13`

Therefore, the radius and slant height of the conical heap are 36 cm and

`12sqrt13` respectively