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Solid of Revolution Cross-Sectional Area

3 Questions

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Solid of Revolution Cross-Sectional Area

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Questions and Answers

What is a solid of revolution?

A 3D object

A curve rotated around an axis (correct)

A function of \(x\

A function of \(y\

How can we determine the cross-sectional area of a solid of revolution?

By calculating the area of the axis of rotation

By using the method of disks

By using the method of rings (correct)

By calculating the volume of the solid

If we rotate about a horizontal axis, what is the cross-sectional area a function of?

\(y\

\(z\

\(x\ (correct)

\(t\

Study Notes

A solid of revolution is a curve that has been rotated about a given axis.
The cross-sectional area of a solid of revolution is a function of the axis of rotation.
If we rotate about a horizontal axis, the cross-sectional area is a function of (x).
If we rotate about a vertical axis, the cross-sectional area is a function of (y).
The method of disks or the method of rings can be used to determine the cross-sectional area of a solid of revolution.

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Description

Test your knowledge of finding the cross-sectional area of solids of revolution using the method of disks or rings, when rotating around both horizontal and vertical axes.