Diameter of ice cream cone 2x = 2(3) = 6cm

Example-12. A solid consisting of a right circular cone standing on a hemisphere, is placed up right in a right circular cylinder full of water and touching the bottom . Find the volume of water left in the cylinder, given that the radius of the cylinder is 3 cm. and its height is 6cm. The radius of the hemisphere is 2 cm. and the height of the cone is 4 cm.

Solution :In the figure drawn here,
ABCD is a cylinder, LMN is a hemisphere and OLM is a cone
We know that when a solid is immersed in the water, then water displaced equal to the volume of the solid.
Volume of the cylinder = pr²h=p x 3² x 6=54 p cm³
Volume of the hemisphere=2/3 pr³=2/3 x p x 2³=16/3 p cm³
Volume of the cone = 1pr2h= 1 ́p ́22 ́4=16pcm3
Volumeofthesolidfigure = 16π+ 16π 33 A3N3B = 32π

Volume of water left in the cylinder
=Volume of Cylinder-Volume of solid figure immersed= 54p - 32p 3 = 162p-32p=130p