(In)finite volumes and areas

Calculus Level 3

Which of these affirmations is true?

A. \ A surface of revolution can have a finite surface area and an infinite volume.
B. \ A surface of revolution can have an infinite surface area and an infinite volume.
C. \ A surface of revolution can have a finite surface area and a finite volume.
D. \ A surface of revolution can have an infinite surface area and a finite volume.

A and B only A and C only A, B, and D only A, C, and D only B and D only B, C, and D only C and D only All of A, B, C, and D are true

Romain Bouchard by Romain Bouchard , 34, France

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1 solution

Michael Mendrin
Jan 14, 2018

B) can be met with a hyperboloid of one sheet

C) can be met with a sphere

D) can be met with Gabriel's Horn

A) is a special case that has been proven to be impossible. See note about the converse of Gabriel's Horn in same article.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

For B, do you mean a paraboloid?

Blan Morrison - 3 years, 4 months ago

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That works too, as well as a cylinder of infinite length. "Hyperboloid of one sheet" was the first thing that popped into my mind.

Michael Mendrin - 3 years, 4 months ago

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