Question

A sphere of diameter $12cm$, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by $3\frac{5}{9}cm$. Find the diameter of the cylindrical vessel.

Answer 1

Increase in the height of the cylinder due to the sphere, $h=3\frac{5}{9}=\frac{32}{9}$ cm

Diameter of sphere $=12$ cm

Radius of the sphere, $R=6$ cm

Rise in the volume of water in cylinder $=$ Volume of sphere

$\pi r^{2}h=\frac{4}{3}\pi R^3$

$r=\sqrt{\frac{4\times 6^3\times 9}{3\times 32}}$

$\therefore r=9$ cm

Therefore, the diameter of the cylindrical vessel $=18$ cm.