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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.
