Question

A solid right-circular cone of height 60 cm and radius 30 cm is dropped in a right-circular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres ?

Answer 1

We have
Height of the cone, h = 60 cm
Radius of base of the cone, r = 30 cm
∴ Volume of the cone\[= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \left( 30 \right)^2 \left( 60 \right) = 18, 000\pi {cm}^3\]

Also, we have
Radius of base of cylinder, R = 60 cm
Height of the cylinder, H = 180 cm

∴ Volume of the cylinder \[= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \left( 30 \right)^2 \left( 60 \right) = 18, 000\pi {cm}^3\]

∴ Volume of water that is left in the cylinder = 648000 \[\pi\] − 18000\[\pi\]

                                         = 630000 ×\[\frac{22}{7}\]

 

                                         = 19,80,000 cm³

                                         =1.98 m³         (1 m³ = 10,00,000 cm³)