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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
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Chapter 6, Problem 32E

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QUESTION:

Problem   32E

Choosing the Washer Method or Shell Method

Find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so

The region bounded by  about

a. the x-axis

b. the y-axis

c. the line x = 4

d. the line y = 2

Questions & Answers

QUESTION:

Problem   32E

Choosing the Washer Method or Shell Method

Find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so

The region bounded by  about

a. the x-axis

b. the y-axis

c. the line x = 4

d. the line y = 2

ANSWER:

Problem 32E

Choosing the Washer Method or Shell Method

Find the volumes of the solids generated by revolving the regions about the given axes. If you think it would be better to use washers in any given instance, feel free to do so

The region bounded by  about

a. the x-axis

b. the y-axis

c. the line x = 4

d. the line y = 2

Step by step solution

Step 1 of 4

(a)

Consider the graph for the given equations as shown in Figure below.

Here, the radius of the shell is y and the height of the shell is .

Also the limit of x is from c=0 to d=2.

Calculate the volume of the solid as,

Solve further as,

Thus, the volume of the solid is .

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