Question

A cylindrical vessel of radius 4 cm contains water. A solid sphere of 3 cm radius is lowered into the water until it is completely immersed. The water level in the vessel will rise by:

• A. \(\frac{2}{9}\)cm
• B. \(\frac{4}{9}\)cm
• C. \(\frac{9}{4}\)cm
• D. \(\frac{9}{2}\)cm

Answer 1

The Correct Option is C

The volume of water displaced by the sphere is equal to the volume of the sphere, which is \[ \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (3)^3 = 36 \pi \, \text{cm}^3. \]

The volume displaced will raise the water level in the cylindrical vessel, which has an area of \[ \pi r^2 = \pi (4)^2 = 16 \pi \, \text{cm}^2. \]

The rise in the water level is given by \[ \frac{\text{volume displaced}}{\text{area of the base}} = \frac{36\pi}{16\pi} = \frac{9}{4} \, \text{cm}. \]