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Questions and Answers
What is a solid of revolution?
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?
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?
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.
