Question

Question 7
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.

Answer 1

Radius of cone = 60 cm, height of cone = 120 cm
Radius of hemisphere = 60 cm
Radius of cylinder = 60 cm, height of cylinder = 180 cm
Volume of cone
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi \times {60}^2\times 120$
$=144000\pi c{m}^3$
Volume of hemisphere
$=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\pi \times {60}^3=144000\pi c{m}^3$
Volume of solid
$=(144000+144000)\pi$
$=288000\pi c{m}^3$
Volume of cylinder
$=\pi r^{2}h$
$=\pi \times {60}^2\times 180$
$=648000\pi c{m}^3$
Volume of water left in the cylinder
$=(648000-288000)\pi$
$=36000\pi$
$=1130400c{m}^3$