# 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.

Given

Radius of cylinder (r) = 18 cm

Height of cylinder (h) = 32 cm

Height of cone (H) = 24 cm

Find out

We have to find the radius and slant height of the heap.

Solution

Let Radius of cone = R

The volume of Cone = Volume of Cylinder

on cancelling π from both sides we get

1/3πR2H = πr2h

1/3R× (24) = 18× 32

R= $\frac{18\times18\times32\times3}{24}$

R = √(18 × 18 × 4)

R = 36 cm

Slant height (l) = √H+ R2

l = √(242 + 362)

l = √(12×2)2 + (12×3)2

l =12 √(4+9)

l = 12 √13 cm

Hence,

Slant height of the heap= 12 √13 cm