Question

A glass cylinder with diameter $20cm$ has water to a height of $9cm$. A metal cube of $8cm$ edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. use $\pi =22/7$

Answer 1

$H=9cm$

$D=20cm,R=\frac{D}{2}=10cm$

side of cube $=8cm$

Total volume of cylinder (after cube is increased)=volume of natur in cylinder + Volume of water

Displaced of volume of cube

$=\pi R^{2}H+a^3$

$=\frac{22}{7}\times 10\times 10\times 9+(8{)}^3$

$=\frac{19800}{7}+512$

$=2828.57+512$

$=3340.57c{m}^3$

Height of water $h1$. It can be found b equating

$\pi R^{2}H1$ with above volume

$\frac{22}{7}\times 10\times 10\times h1=3340.57$

$h1=23303.99/2200$

$h1=10.63cm$

Rise in the water level in the cylinder $=h1-H$

$=10.63-9$

$=1.63cm$