- #1

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- Thread starter americanforest
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- #1

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- #2

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Use the integration techniques from multivariable calc.

- #3

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Given the vaugeness of the question, I would be tempted to just integrate the volume parameterised by

[tex]S(r,\theta,z_1,z_2,\ldots,z_n) = (r\cos{\theta},r\sin{\theta},z_1,z_2,\ldots,z_n)[/tex]

But I think the question you might have been asked was to find the volume of a hyper*sphere*. That's easily googled. And has a few interesting properties as you move through the dimensions

[tex]S(r,\theta,z_1,z_2,\ldots,z_n) = (r\cos{\theta},r\sin{\theta},z_1,z_2,\ldots,z_n)[/tex]

But I think the question you might have been asked was to find the volume of a hyper

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- #4

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Partition your object into pieces whose volumes are easier to calculate... then add them up. That it wraps around onto itself shouldn't be a problem as long as you don't double count any volumes. (The lateral area of a cylinder ("the soup label") is the same as the area of the associated rectangle.)