Question

A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by $2cm$. If the area of the base of the cuboid is $160{cm}^2$ and its height $12cm$, determine the radius of any of the spheres.

Answer 1

Let the radius of each sphere be $r$ $cm$

Volume of a sphere $=\left(\frac{4}{3}\pi r^3\right)$ $c{m}^3$

Increase in volume of the cuboid $=162\times 2$ $c{m}^2$

It is known that increase in volume of the cuboid will be equal to the volume of all three spheres.

$160\times 2=3\left(\frac{4}{3}\pi r^3\right)$

$320=3(\frac{4}{3}\times \frac{22}{7}\times r^3)$

$r^3=25.45$

$\Rightarrow r=2.94$ $cm$