Question

A sphere of diameter 12 cm, 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 $\frac{32}{9}cm$.

Find the diameter of the cylindrical vessel.

Answer 1

Given, diameter of sphere = 12 cm

then, radius of sphere $\left(r\right)=\frac{12}{2}=6cm$

Volume of sphere = $\frac{4}{3}\pi r^3$

= $\frac{4}{3}\times \pi \times (6{)}^{3}c{m}^3$

Now, sphere is completely submerged in water and rise in water in cylindrical vessel is $3\frac{5}{9}$cm.

Volume of sphere = Volume of cylindrical vessel

$\frac{4}{3}\pi \times (6{)}^3=\pi r^2\times \frac{32}{9}$

$r^2=\frac{4\times 6\times 6\times 6\times 9}{3\times 32}$

$r=\sqrt{81}$

$r=9cm$

$\therefore$ Diameter of the cylindrical vessel is 18 cm.