Question

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 7 cm in it. The increase in the height of water in the container is :

• A. 9.33 cm
• B. 4.5 cm
• C. 10.1 cm
• D. 28 cm

Answer 1

The correct option is A 9.33 cm

Given, radius of the cylindrical vessel (R) is 7 cm and its height is 14 cm.
Radius of the spherical ball, r = 7 cm

Let the increase in height of water in the container be 'H' cm.

Volume of the water risen = Volume of the sphere
$\pi R^{2}H=\frac{4}{3}\pi r^3$
$\frac{22}{7}\times {\left(7\right)}^2\times H=\frac{4}{3}\times \frac{22}{7}\times {\left(7\right)}^3$
$\Rightarrow H=\frac{4}{3}\times 7$
$\Rightarrow H=9.33cm$