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.

Answer 1

Let's find the height by which water will rise in the cylinder.

Diameter of the cylinder $=20cm$

Height of the water in the cylinder $=9cm$

So, the radius of the cylinder $=\frac{20}{2}=10cm$

Suppose the water rises by $h$ cm

Volume of water displaced $=$ Volume of the cube of edge $8cm$

${\mathrm{\pi r}}^2\mathrm{h}=8^3$

$$\begin{gathered} \frac{22}{7}\times {10}^2\times h=8\times 8\times 8 \\ \frac{22}{7}\times {10}^2\times h=512 \\ h=\frac{\left(512\times 7\right)}{\left(22\times 100\right)} \\ Weget, \\ h=1.629cm \end{gathered}$$

Hence, the height by which water will rise in the cylinder.