An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm. When a few solid spherical metallic balls each of radius 1/2 cm are dropped in the vessel, 25% water is overflowed. The number of balls is:

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& 25\%\text{ of }\left(\text{Volume of cone}\right)=x\times \text{ volume of sphere}\\ & \frac{1}{4}\times \frac{1}{3}\pi r^{2}h=x\times \frac{4}{3}\pi R^3\\ & \frac{1}{4}\times \frac{1}{3}\pi \times 5\times 5\times 8=x\times \frac{4}{3}\pi \times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\ & x=100\end{array}$$