Question

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.

Answer 1

The object is shown in the figure below. 

Radius of hemisphere = 2.1 cm

Volume of hemisphere = `2/3 pir^3 = 2/3 xx 22/7 xx2.1xx2.1=19.404  "cm"^3`

Height of cone = 4 cm 

Volume of cone = `1/3 pir^2h =1/3xx22/7xx2.1xx2.1xx 4=18.48   "cm"^3 `

When the object is immersed in the tub, volume of water equal to the volume of the object is displaced from the tub.

Volume of water left in the tub = 770 - 37.884 = 732.116 cm³