Question

A sphere of diameter $6cm$ is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is $13cm$. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel

Answer 1

We have
Radius of sphere $=3cm$
$\text{Volume of the sphere}=\frac{4}{3}\pi \times {\left(3\right)}^3{cm}^3=36\pi {cm}^3[V=\frac{4}{3}\pi r^3]$

Radius of the cylindrical vessel $=6cm$

Suppose the water level rises by $h$ cm in the cylindrical vessel.

Then volume of the cylinder of height $h$ cm and radius $6cm$ is given as

$(\pi \times 6^2\times h){cm}^3=36\pi h{cm}^3$

Clearly volume of water displaced by the sphere is equal to the volume of the sphere

$\therefore 36\pi h=36\pi$

$\Rightarrow h=1cm$