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 $\frac{32}{9}cm$. The diameter of the cylindrical vessel is _____.

• A. $12cm$
• B. $14cm$
• C. $16cm$
• D. $18cm$

Answer 1

The correct option is D $18cm$

Given,
Diameter of sphere, $d=12cm$
So, radius of sphere, $r=\frac{12}{2}=6cm$

Volume of sphere
$=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times (6{)}^3$

It is given that the sphere is completely submerged in water and rise in water in cylindrical vessel is $\frac{32}{9}cm$.

So,
Volume of sphere = volume of water rise in the cylindrical vessel
$\Rightarrow \frac{4}{3}\pi \times 6^3=\pi r^2\times \frac{32}{9}$
$\Rightarrow r^2=\frac{4\times 6\times 6\times 6\times 9}{3\times 32}$
$\Rightarrow r=\sqrt{81}$
$\Rightarrow r=9cm$

So, the diameter of the cylindrical vessel is $18cm$.