The first step is to determine the volume of the cone. The formula for determining the volume of a cone is expressed as
V = 1/3 * pi * r^2h
Given that
h = 8
r = 5
Volume of cone = 1/3 * 3.14 * 5^2 * 8
Volume of cone = 209.33
Since the cone is filled to the brim, the volume of water inside is 209.33 cm^3
The next step is to determine the voluem of each lead shot. We would apply the formula for determining the volume of a sphere which is expressed as
Volume of sphere = 4/3 * pi * r^3
Given that r = 0.5cm,
Volume of sphere = 4/3 * 3.14 * 0.5^3
Volume of sphere = 0.523 cm^3
If 1/4 of the water flows out, it means that the amount of water that flowed out is
1/4 * 209.33 = 52.3325
The volume of water that flowed out is equivalent to the volume of the lead shots that were dropped inside the vessel. The number of lead shots would be
52.3325/0.523 = 100.1
Approximately 100 lead shots were dropped inside the vessel.