Question

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. [Use \(\pi=\frac{22}{ 7} \)]

Answer 1

Hemisphere radius (r) = Cone radius (r) = 60 cm
Cone height (h₂) = 120 cm
Cylinder height (h₁) = 180 cm
Cylinder radius (r) = 60 cm

Water remaining = Cylinder volume - Solid volume
= Cylinder volume - (Cone volume + Hemisphere volume)
\(=\pi r^2h_1−\left [\frac{1}{3}\pi r^2h_2+\frac{2}{3}\pi r^3\right]\)

\(=\pi ×(60)^2×(180)−\left[\frac{1}{3}\pi ×(60)^2×120+\frac{2}{3}\pi×(60)^3\right]\)

\(=\pi (60)^2\left[180−(40+40)\right]\)
\(=\pi (3600)\left[100\right]\)
\(=3,60,000×227\)
\(=1131428.57 cm^3\)
\(=1.131 m^3\)