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

radius of the hemisphere = 2.1 cm.

height of the cone = 4 cm

radius of the cone = 2.1 cm

Volume of the solid = Vol(cone) + Vol(hemisphere)

$\text{Volume of the solid}=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3=\frac{1}{3}\pi r^2(h+2r)=\frac{1}{3}\pi \left(2.1{)}^2\right(4+2\times 2.1)=12.054\pi$

Radius of cylinder = 5 cm

Height of the cylinder = 9.8 cm

Volume of the cylinder $=\pi r^{2}h=\pi \left(5{)}^2\right(9.8)=245\pi$

Volume of water displaced = Volume of the solid

So,

Volume of water left in cylindrical tub = Volume of cylinder - Volume of solid

$\text{Volume of water left in cylindrical tub}=245\pi -12.054\pi =232.946\times 3.14=731.45c{m}^3$