Question

A square is rotated about an axis lying in the plane of the square, which intersects thesquare only at one of its vertices. For what position of the axis, is the volume of theresulting solid of revolution the largest

Answer 1

Answer:

I think you want Pappus's (2nd) Centroid Theorem: the volume of a planar area of revolution is the product of the area A and the length of the path traced by its centroid R, i.e., 2πR. The bottom line is that the volume is given simply by V=2πRA.

Since the area is fixed, and the maximum distance of the centroid is at θ=45∘, then your intuitive solution is correct.

Step-by-step explanation:

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