Question

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged then the water level rises by

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Answer 1

Let r and R be the radius of the sphere and cylindrical vessel respectively.

Given, $2r=18cm\Rightarrow r=9cm2R=36cm\Rightarrow R=18cm$

Let the rise in water level in the cylindrical vessel be h cm.

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

The volume of liquid displaced in the cylindrical vessel $=\pi R^{2}h$

If the sphere is completely submerged in the vessel, then

The volume of liquid displaced in the cylindrical vessel = Volume of the sphere

$\pi R^{2}h=\frac{4}{3}\pi r^3\Rightarrow {18}^2\times h=\frac{4}{3}\times 9^2\Rightarrow h=\frac{4\times 9^2}{3\times {18}^2}=3cm$

Thus, the rise in water level in the cylindrical vessel is 3 cm.