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 bottoms . How many litres of water is left in the cylinder, If the radius of the cylinder is 60 cm and its height is 180 cm .

Answer 1

REF.Image

The volume of water left in cylinder will be :

(x-z)

$\Rightarrow \pi r^{2}h-\frac{1}{2}\times \frac{4}{3}\times \pi r^3$

$\Rightarrow \pi \times {60}^2\times 60-\frac{2}{3}\pi \times {60}^2$

$\Rightarrow \frac{1}{3}\times \pi \times {60}^3$

volume left = $226,194.67c{m}^2$