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) $\frac{2}{9}$ cm

(b) $\frac{4}{9}$ cm

(c) $\frac{9}{4}$ cm

(d) $\frac{9}{2}$ cm

Answer 1

The radius of sphere, r = 3 cm

The volume of sphere

$$\begin{gathered} =\frac{4}{3}{\mathrm{\pi r}}^3 \\ =\frac{4}{3}\mathrm{\pi }{\left(3\right)}^3 \\ =36\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

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

Hence, the correct answer is choice (c).