Technical Mathematics, Sixth Edition

Chapter 17. Ratio, Proportion, and Variation

OBJECTIVES When you have completed this chapter, you should be able to Set up and solve a proportion for a missing quantity. Solve applied problems using proportions. Find dimensions, areas, and volumes of similar geometric figures. Set up and solve problems involving direct variation, inverse variation, joint variation, and combined variation. Solve applied problems involving variation. Set up and solve power function problems.

We earlier described a ratio as the quotient of two quantities, say a/b. Here we will set one ratio equal to another to get a proportion. We will learn how to solve proportions for a missing quantity.

We next apply the idea of proportions to the very important subject of similar figures. In technology we often have to relate an actual object to a drawing or model of that object—from a machine part to an engineering drawing of that part, from a geographical area to a map of that area, from a building to a scale model of that building. How do dimensions, areas, and volumes on one relate to those on the other? For example, if a one-fourth scale model of a space probe, Fig. 17-1, has a surface area of 13.5 m², what is the surface area of the actual probe? Here we give you the tools to handle such problems.

When two quantities, say, x and y, are connected by some functional relation, y = f(x) some variation in the independent variable x will cause a variation in the dependent variable y. In our study of functional variation ...