a.
To find:The volume of the solid generated by resolving the region bounded by the curves.
a.
Answer to Problem 36E
The volume of the solid generated is
Explanation of Solution
Given information:
The indicated axis is
Formula used:
There are two formulas that can be applied, depending on the strip utilized or the axis of revolution, to calculate the volume of the solid of revolution using the cylindrical shell method.
Recall that the strip to be utilized in the cylindrical shell method must be parallel to the axis of revolution.
For horizontal strip (rotated about the
For vertical strip (rotated about the
Calculation:
Let's first create a graph showing the region that will be rotated about the
From the graph, the limits of integration is bounded from
The height of the strip is given by,
From the given axis let’s use the horizontal strip,
Therefore, the volume of the solid generated is
b.
To find: The volume of the solid generated by resolving the region bounded by the curves.
b.
Answer to Problem 36E
The volume of the solid generated is
Explanation of Solution
Given information:
The line
Formula used:
There are two formulas that can be applied, depending on the strip utilized or the axis of revolution, to calculate the volume of the solid of revolution using the cylindrical shell method.
Recall that the strip to be utilized in the cylindrical shell method must be parallel to the axis of revolution.
For horizontal strip (rotated about the
For vertical strip (rotated about the
Calculation:
Let's first create a graph showing the region that will be rotated about
From the graph, the limits of integration is bounded from
The height of the strip is given by,
From the given axis let’s use the horizontal strip,
Therefore, the volume of the solid generated is
c.
To find: The volume of the solid generated by resolving the region bounded by the curves.
c.
Answer to Problem 36E
The volume of the solid generated is
Explanation of Solution
Given information:
The line
Formula used:
There are two formulas that can be applied, depending on the strip utilized or the axis of revolution, to calculate the volume of the solid of revolution using the cylindrical shell method.
Recall that the strip to be utilized in the cylindrical shell method must be parallel to the axis of revolution.
For horizontal strip (rotated about the
For vertical strip (rotated about the
Calculation:
Let's first create a graph showing the region that will be rotated about
From the graph, the limits of integration is bounded from
The height of the strip is given by,
From the given axis let’s use the horizontal strip,
Therefore, the volume of the solid generated is
d.
To find: The volume of the solid generated by resolving the region bounded by the curves.
d.
Answer to Problem 36E
The volume of the solid generated is
Explanation of Solution
Given information:
The line
Formula used:
There are two formulas that can be applied, depending on the strip utilized or the axis of revolution, to calculate the volume of the solid of revolution using the cylindrical shell method.
Recall that the strip to be utilized in the cylindrical shell method must be parallel to the axis of revolution.
For horizontal strip (rotated about the
For vertical strip (rotated about the
Calculation:
Let's first create a graph showing the region that will be rotated about
From the graph, the limits of integration is bounded from
The height of the strip is given by,
From the given axis let’s use the horizontal strip,
Therefore, the volume of the solid generated is
Chapter 7 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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