CalculusVolume2-SASG-02-03
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 2
Applications of Integration
2.3 Volumes of Revolution: Cylindrical Shells
Section Exercises
For the following exercise, find the volume generated when the region between the two curves is rotated around the given axis. Use both the shell method and the washer method. Use technology to graph the functions and draw a typical slice by hand.
115.
[T] Under the curve of rotated around the Answer:
units
3
117.
[T] Under the curve of rotated around the Answer:
units
3
119.
[T] Under the curve of rotated around the
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, use shells to find the volumes of the given solids. Note that the rotated regions lie between the curve and the x
-axis and are rotated around the y
-axis.
121.
Answer:
units
3
123.
Answer:
units
3
125.
Answer:
units
3
127.
Answer:
units
3
129.
Answer:
units
3
For the following exercises, use shells to find the volume generated by rotating the regions between the given curve and around the x
-axis.
131.
Answer:
units
3
133.
Answer:
units
3
135.
Answer:
units
3
137.
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Answer:
units
3
139.
(one lobe in the first quadrant only)
Answer:
units
3
For the following exercises, find the volume generated when the region between the curves is rotated around the given axis.
141.
rotated around the
Answer:
units
3
143.
rotated around the line
Answer:
units
3
145.
rotated around the
Answer:
units
3
147.
rotated
around the
Answer:
149.
[T] Left of right of around the Answer: units
3
For the following exercises, use technology to graph the region. Determine which method you think would be easiest to use to calculate the volume generated when the function is rotated around the specified axis. Then, use your chosen method to find the volume.
151.
[T]
rotated around the
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
units
3
153.
[T]
rotated around the
Answer:
units
3
155.
[T] rotated around the
Answer:
units
3
157.
[T]
rotated around the
Answer:
OpenStax Calculus Volume 2
Student Answer and Solution Guide
units
3
Your preview ends here
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, use the method of shells to approximate the volumes of some common objects, which are pictured in accompanying figures.
159.
Use the method of shells to find the volume of a cone with radius
and height
Answer: units
3
161.
Use the method of shells to find the volume of a cylinder with radius and height .
Answer:
units
3
163.
Consider the region enclosed by the graphs of and
. What is the volume of the solid generated when this region is rotated around the
Assume that the function is defined over the interval .
Answer:
units
3
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