Question

A cylindrical bucket, 32 cm high and 18 cm of 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, find the radius and slant height of the heap.

Answer 1

Given,

Height of the cylindrical bucket = 32 cm

Radius of the cylindrical bucket = 18 cm

Height of conical heap = 24 cm

We know that,

Volume of cylinder = π × r² × h

And, volume of cone = 1/3 π × r² × h

Then, from the question

Volume of the conical heap = Volume of the cylindrical bucket

1/3 π × r² × 24 = π × 18² × 32

r² = 18² x 4

r = 18 x 2 = 36 cm

Now,

Slant height of the conical heap (l) is given by

l = √(h² + r²)

l = √(24² + 36²) = √1872

l = 43.26 cm

Therefore, the radius and slant height of the conical heap are 36 cm and 43.26 cm respectively.