A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.
A solid is in the form of a right circular cone mounted on a hemisphere.
Let r be the radius of hemisphere and cone
Let h be the height of the cone
Radius of hemisphere = r = 2.1 cm
Volume of hemisphere = 2/3 πr3
= 2/3 × 22/7 × 2.1 × 2.1 × 2.1 cm3
= 19.404 cm3
Height of cone = h = 4 cm
Radius of cone = r = 2.1 cm
Volume of cone = 1/3 πr2h
= 1/3 × 22/7 × 2.1 × 2.1 × 4 cm3
= 18.48 cm3
Volume of solid = Volume of hemisphere + Volume of cone
= 19.404 cm3 + 18.48 cm3 = 37.884 cm3
The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water, so, to find the volume of water left in the tub we need to subtract volume of solid from cylindrical tub.
Radius of cylinder = r’ = 5 cm
Height of cylinder = h’ = 9.8 cm
Volume of cylindrical tub = πr’2h’ = 22/7 × 5 × 5 × 9.8 cm3
= 770 cm3
Volume of water left in the tub = Volume of cylindrical tub – Volume of solid
Volume of water left in the tub = 770 cm3 – 37.884 cm3 = 732.116 cm3
∴ Volume of water left in the tub is 732.116 cm3