Wilson Ncaa
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Wilson Ncaa
Softball math question?
An NCAA-regulation softball is in the shape of a sphere with diameter 4 inches. Traditionally, a softball is filled with a cork-like substance and is covered with a leather cover ("softballs" really are not all that soft!). The Wilson Sporting Goods company manufactures these softballs in lots of 10,000.
a. Assuming no waste, how much leather is needed for one lot of softballs? Please give your answer
both in square inches and in square feet (1 sq ft = 144 sq in).
b. Assuming no waste, how much cork-like substance is needed for one lot of softballs? Please give
your answer both in cubic inches and cubic feet (1 cu ft = 1728 cu inches).
A)
The formula for the surface area of a sphere is:
a = 4 * pi * radius²
So the surface area (in inches) of one softball is:
a = 4 * pi * 2² = 25.12 square inches
For 10,000 softballs:
25.12 * 10,000 = 251,200 square inches
In terms of square feet:
251,200 / 144 = 1,744.44 square feet
B)
The formula for the volume of a sphere is:
v = 4 / 3 * pi * radius³
So the volume (in inches) of one softball is:
v = 4 / 3 * pi * 2³ = 33.49 cubic inches
For 10,000 softballs:
33.49 * 10,000 = 334,900 cubic inches
In terms of cubic feet:
334,900 / 1,728 = 193.81 cubic feet