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

The height and radius of the cylindrical bucket arecm andcm respectively. Therefore, the volume of the cylindrical bucket is

The bucket is full of sand and is emptied in the ground to form a conical heap of sand of height cm. Let, the radius and slant height of the conical heap be cm and cm respectively. Then, we have

The volume of the conical heap is

Since, the volume of the cylindrical bucket and conical hear are same, we have

Then, we have

Therefore, the radius and the slant height of the conical heap are 36 cm and 43.27 cm respectively.