Question

In a cylindrical vessel of diameter 24 cm filled up with sufficient quantity of water. A solid spherical ball of radius 6 cm is completely immersed. Then the increase in height of water level is:

• A. 1.5 cm
• B. 2 cm
• C. 3 cm
• D. cm

Answer 1

Answer: (B)

2 cm

Let the increase in height of water level be $h$.

Given quantities:

Radius of sphere, $R=6\text{cm}$

Radius of cylinder, $r=\frac{24}{2}\text{cm}=12\text{cm}$

The increase in volume of water will be equal to volume of ball immersed:

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

$\pi (12{)}^{2}h=\frac{4}{3}\pi (6{)}^3$

$h=2\text{cm}$