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(Please review Chapter 9 in the College Math text for geometric objects
and their properties.) For a familiar example, the perimeter and area
formulas for a rectangle are mathematical models for distance around the
rectangle (perimeter) and area enclosed by the sides, respectively; P =
2L + 2W and A = L x W. For another example, the volume of a rectangular
box would be: V = L x W x H, where L = Length, W = Width, and H =
Height. The surface area of a rectangular box would be: SA = 2(L x W) +
2(W x H) + 2(L x H). Your problem is to obtain (or make) a rectangular
box with a top on it that has the smallest possible surface area and
that a football and a basketball, both fully inflated, will just fit
into at the same time. What could make a good model for
this situation? Using Polya’s technique for solving problems, describe
and discuss the strategy, steps, and procedures you will use to solve
this problem. Then, demonstrate that your solution is correct.
