Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely. Then the height of the glass (in cm) is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Radius of water drop}} = \frac{1}{{20}}{\text{ cm}} \cr & {\text{Volume of a sphere}} = \frac{4}{3}\pi \times \frac{1}{{20}} \times \frac{1}{{20}} \times \frac{1}{{20}} \cr & {\text{Let the radius of cone}} = R \cr & {\text{Height}} = 2R \cr & {\text{According to question}} \cr & \frac{1}{3}\pi \times R \times R \times 2R = \frac{4}{3}\pi \times \frac{1}{{20}} \times \frac{1}{{20}} \times \frac{1}{{20}} \cr & {R^3} = \frac{{2 \times 32000}}{{20 \times 20 \times 20}} \cr & {R^3} = \frac{{64000}}{{20 \times 20 \times 20}} \cr & {R^3} = \frac{{40 \times 40 \times 40}}{{20 \times 20 \times 20}} \cr & R = \frac{{40}}{{20}} \cr & R = 2 \cr & {\text{Height of glass}} = 2R = 2 \times 2 = 4{\text{ cm}} \cr} $$