Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 9 - Section 9.3 - Cylinders and Cones - Exercises - Page 432: 32

Answer

The total area is $2\pi r(r+h)$

Work Step by Step

In order to obtain this formula, we consider the bases. Since they are both circles, their combined area is $2\pi r^2$. We now consider the side. Its area equals the circumference of the base circles times the height, which is the same as $2\pi rh$. We add these areas and simplify to find: $ A = 2\pi r^2 + 2\pi rh = 2\pi r(r+h)$
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