General Collage Mathermatics

MATH125: Unit 1 Individual Project

Mathematical Modeling and Problem Solving

All commonly used formulas for geometric objects are really mathematical models of the characteristics of physical objects. For example, the characteristic of the volume inside a common closed cardboard box can be modeled by the formula for the volume of a rectangular solid, V = L x W x H, where L = Length, W = Width, and H = Height of the box. A basketball, because it is a sphere, can be partially modeled by its distance from one side through the center to the other side, or diameter, by the diameter formula for a sphere, D = 2r.

Complete onlyONE of the following questions.

1. (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.