Question

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Answer 1

We have,
Radius of cylinder = Radius of cone = Radius of hemisphere = 60 cm
Height of cone = 120 cm
Height of cylindrical vessel = 120 + 60 = 180 cm

Volume of cylinder =πr²h =22/7 x(60)² x180

Now, volume of the solid
= Volume of cone + Volume of hemisphere

Volume of water left in the cylinder
= Volume of the cylinder – Volume of the solid