Question

A solid right circular  cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone 

Answer 1

Height of the cone, h = 120 cm
Radius of the cone, r = 60 cm
Height of the cylinder, H = 180 cm
Radius of the cylinder, R = 60 cm
Volume of the cylinder =  \[\pi R^2 H = \pi \left( 60 \right)^2 \times 180 {cm}^3\]

Volume of the cone = \[\frac{1}{3} \pi r^2 h = \frac{1}{3}\pi \left( 60 \right)^2 \times 120\]

Volume of water left in the cylinder = Volume of cylinder − volume of the cone 

\[= \pi \left( 60 \right)^2 \times 180 - \frac{1}{3}\pi \left( 60 \right)^2 \times 120\]

\[ = \pi \left( 60 \right)^2 \left[ 180 - 40 \right]\]

\[ = \pi \times 3600\left[ 140 \right]\]

\[ = 1584000 {cm}^3 \]

\[ = 1 . 584 m^3\]