Explanation 1) Concept: i. If the cross section is a washer with the inner radius r i n and outer radius r o u t , then the area of the washer is obtained by subtracting the area of the inner disk from the area of the outer disk. A = π o u t e r r a d i u s 2 - π i n n e r r a d i u s 2 ii. The volume of solid revolution about y -axis V = ∫ a b A ( y ) d y 2) Given: The region is bounded by x = 0 , x = 9 - y 2 rotated about the line x = - 1 3) Calculation: As the region is bounded by x = 0 , x = 9 - y 2 rotated about the line x = - 1 , From the figure, as the region rotates about the line = - 1 , the strip is perpendicular to y -axis. A cross section of the solid is the washer with outer radius is 9 - y 2 - - 1 = 10 - y 2 (distance from x = - 1 to x = 9 - y 2 ) and inner radius is 0 - - 1 = 1 , which is the distance from x = - 1 to x = 0 . So its area is given by A y = π o u t e r r a d i u s 2 - π i n n e r r a d i u s 2 = π 10 - y 2 2 - π 1 2 = π 100 - 20 y 2 + y 4 - 1 A ( x ) = π 99 - 20 y 2 + y 4 The region of integration is bounded by x = 0 , x = 9 - y 2 Therefore, 9 -

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.R, Problem 9E

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To find:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line and sketch the region, the solid, and a typical disk or washer.

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Chapter 5.R, Problem 8E

Chapter 5.R, Problem 10E

Chapter 5 Solutions

Calculus (MindTap Course List)

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Prob. 3E Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 10E

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The volume of the solid obtained by rotating the region bounded by the given curves about the specified line and sketch the region, the solid, and a typical disk or washer.

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To find: The volume of the solid obtained by rotating the region bounded by the given curves about the specified line and sketch the region, the solid, and a typical disk or washer.

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Chapter 5 Solutions

To find:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line and sketch the region, the solid, and a typical disk or washer.