Question

A cylindrical vessel of radius $4cm$ contains water. a solid sphere of radius $3cm$ is lowered 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 $\frac{9}{4}cm$

Volume of sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \frac{22}{7}\times 3\times 3\times 3$

$=\frac{36\times 22}{7}$

$\therefore \frac{36\times 22}{7}c{m}^3$ water displaced

There will be $\frac{36\times 22}{7}c{m}^3$ rise

Vol cylinder $=\pi r^{2}h$

$\frac{36\times 22}{7}=\frac{22}{7}\times 16\times h$

$\frac{36\times 22}{22\times 16}=h$

$h=\frac{9}{4}cm$.