Question

Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap. 

Answer 1

Height of the cylinder = h1 = 32 cm
Radius of bucket = r1 = 18 cm 
Height of conical heap = h2 = 24 cm 
Let radius of conical heap = r2 

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

⇒ `pi xx r1^2 xx h1 = 1/3 xx pi xx r2^2 xx h2`

⇒ `18 xx 18 xx 32 = 1/3 xx r2^2 xx 24`

⇒ `r2^2 = (10368 xx 3)/24`

⇒ `r2^2 = 1296`

⇒r2 = 36 cm

Radius of the conical heap = 36 cm