Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 4 - An Introduction to Functions - 4-1 Using Graphs to Relate Two Quantities - Practice and Problem-Solving Exercises - Page 244: 17


V = $\frac{4}{3}$$\pi$$r^{3}$ that gives Volume as a function of radius has radius as the independent variable and the volume as the dependent variable. The graph of this function is given below.

Work Step by Step

The radius, r, is the independent variable because the volume is dependent on the radius as if we manipulate the value of radius of the sphere, we can change the volume of the sphere. For example if the radius is r=1, the volume is V(1)=$\frac{4}{3}$$\pi$$(1)^{3}$= $\frac{4}{3}$$\pi$ If the radius is r=2, the volume is V(2)=$\frac{4}{3}$$\pi$$(2)^{3}$= $\frac{4}{3}$$\pi$$\times$8= $\frac{32}{3}$$\pi$ Therefore, if the radius of the sphere is changed, the volume of the sphere is is affected.
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