Question

A cylindrical container with a diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions $22cm\times 14cm\times 10.5cm$. Find the rise in the level of the water when the solid is sub-merged.

Answer 1

When the solid is submerged in water it displaces its own volume.

The volume of the rectangular block is :
Volume = Length × Width × height

Volume =$22cm\times 14cm\times 10.5cm$ = 3234 $c{m}^3$

The volume of a cylinder = $\frac{22}{7}\times r^2\times h$

The rise in height is :

3234 = $\frac{22}{7}\times 21\times 21\times h$

3234 = $22\times 21\times 3\times h$

3234 = $22\times 63\times h$

h = $\frac{3234}{22\times 63}$


h = 49 cm
The water rises by 49 cm