Question:
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by
(a) $\frac{2}{9} \mathrm{~cm}$
(b) $\frac{4}{9} \mathrm{~cm}$
(c) $\frac{9}{4} \mathrm{~cm}$
(d) $\frac{9}{2} \mathrm{~cm}$
Solution:
The radius of sphere, r = 3 cm
The volume of sphere
$=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \pi(3)^{3}$
$=36 \pi \mathrm{cm}^{3}$
Since,
The sphere fully immersed into the vessel, the level of water be raised by x cm.
Then,
The volume of raised water = volume of sphere
$x=\frac{9}{4} \mathrm{~cm}$
Hence, the correct answer is choice (c).