Question

A cylindrical vessel of diameter $4$ cm is partly filled with water. $300$ lead balls are dropped in it. The rise in water level is $0.8$ cm. The diameter of each ball is __________.

• A. $0.8$ cm
• B. $0.4$ cm
• C. $0.2$ cm
• D. $0.5$ cm

Answer 1

Answer: (B)

$0.4$ cm

Diameter of the vessel $=4$ cm

Radius of vessel $=2$ cm

Rise in water level $=0.8$ cm

Volume of the increased water level $=\pi r^{2}h=\frac{22}{7}\times (2{)}^2\times 0.8=10.06$ cu.cm

Volume of $300$ balls $=300\times \frac{4}{3}\times \frac{22}{7}\times (r{)}^3$

$\Rightarrow r^3=10.06\times \frac{1}{300}\times \frac{3}{4}\times \frac{7}{22}$

$\Rightarrow r^3=0.008$

$\Rightarrow r=0.2$

So, the radius of each ball is $0.2$ cm.

Diameter of each ball is $2\times 0.2=0.4$ cm.