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 $$\frac{1}{2}$$ cm are dropped in the vessel, 25% water is overflowed. The number of balls is:

Solution (By Examveda Team)

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