A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Explanation

To solve the problem, we need to find the number of lead shots that can be dropped into the inverted conical vessel without exceeding the volume of water that flows out when one-fourth of the water is displaced. Here is a step-by-step solution:

### Step 1: Calculate the volume of the conical vessel.
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
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