CalculusVolume2-SASG-02-02
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
Chapter 2
Applications of Integration
2.2 Determining Volumes by Slicing
Section Exercises
59.
Use the slicing method to derive the formula for the volume of a cone.
Answer: This is a proof; therefore, no answer is provided.
61.
Use the disk method to derive the formula for the volume of a trapezoidal cylinder.
Answer: This is a proof; therefore, no answer is provided.
For the following exercises, draw a typical slice and find the volume using the slicing method for the given volume.
63.
A pyramid with height 6 units and square base of side 2 units, as pictured here.
Answer: 8 units
3
65.
A tetrahedron with a base side of 4 units, as seen here.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
67.
A cone of radius and height has a smaller cone of radius and height removed from the top, as seen here. The resulting solid is called a frustum
.
Answer:
units
3
For the following exercises, draw an outline of the solid and find the volume using the slicing method.
69.
The base is a triangle with vertices and Slices perpendicular to the xy
-plane are semicircles.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
71.
The base is the region under the parabola
and above the Slices perpendicular to the
are squares.
Answer:
units
3
73.
The base is the area between
and
Slices perpendicular to the x
-axis are semicircles.
Answer:
units
3
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, draw the region bounded by the curves. Then, use the disk method to find the volume when the region is rotated around the x
-axis.
75.
Answer:
units
3
77.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
79.
Answer:
units
3
81.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the y
-axis.
83.
Answer:
units
3
85.
Answer:
units
3
87.
Answer:
units
3
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
89.
Answer:
units
3
For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the x
-axis.
91.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
93.
Answer:
units
3
95.
Answer:
units
3
97.
Answer:
units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
For the following exercises, draw the region bounded by the curves. Then, use the washer method to find the volume when the region is revolved around the y
-axis.
99.
Answer:
units
3
101.
Answer:
units
3
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
103.
Yogurt containers can be shaped like frustums. Rotate the line
around the y
-axis to find the volume between .
Answer:
units
3
105.
Rotate the ellipse
around the y
-axis to approximate the volume of a
football.
Answer: units
3
OpenStax Calculus Volume 2
Student Answer and Solution Guide
107.
What is the volume of the Bundt cake that comes from rotating around the y
-
axis from to ?
Answer:
units
3
For the following exercises, find the volume of the solid described.
109.
The base is the region enclosed by the generic ellipse
. Slices perpendicular to the x
-axis are semicircles.
Answer: units
3
111.
Find the volume common to two spheres of radius with centers that are
apart, as shown here.
OpenStax Calculus Volume 2
Student Answer and Solution Guide
Answer:
units
3
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OpenStax Calculus Volume 2
Student Answer and Solution Guide
113.
Find the volume of a sphere of radius
with a cap of height
removed from the top, as seen here.
Answer:
units
3
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