Question

A solid right cylinder cone of radius $30cm$ and height 60cm is dropped in a right circular cylinder of radius 60cm full of Water upto a height of $180$ cm. Find the rise in level of water.

Answer 1

Given: A solid right cylinder cone of radius $r=30cm$ and height $h=60cm$ is dropped in a right circular cylinder of radius $R=60cm$ full of Water upto a height of $H=180cm$.

So we have,
$r=30cm,R=60cm$
$h=60cm,H=180cm$

$Vol.ofwaterleftincylinder=Vol.ofthecylinder-vol.ofcone$

$Vol.ofcylinder=\pi \times R^2\times h$
$=\pi \times 60\times 60\times 180$
$=\pi 648000$

$Vol.ofcone=\frac{1}{3}\pi \times R^2\times h$
$=\pi \times \frac{1}{3}\times 30\times 30\times 60$
$=\pi 18000$

Now,
$Vol.ofwaterleftincylinder=\pi (648000-18000)$
$=\frac{22}{7}\times 630000$ [Take, $\pi =\frac{22}{7}$]
$=22\times 90000$
$=1980000c{m}^3$

Therefore, the amount of water that went off is $1980000c{m}^3$.