Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 35: 135

Answer

see explanation

Work Step by Step

It helps to visualize something like toilet paper Thickness is $R-r (outside - inside)$ Average radius is $\frac{R+r}{2}$ (average of two) formula given is $ V=\pi{R}^{2}h-\pi{r}^{2}h$ Factor out common factor $ \pi{h}$ $V= \pi{h}(R^{2}-r^{2})$ Use special product formula [ $A^{2}-B^{2} =(A-B)(A+B)$] $V=\pi{h}(R-r)(R+r)$ Remember (R-r) is the thickness (R+r) is 2 x average radius h is height So we have $V= \pi(height)(thickness)(2average Radius)$ Rearrange $ V= 2\pi*average Radius*height*thickness$
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