What is the ratio of the base areas of cone and cylinder under certain constraints?

von The Library of Congress

Frage von : What is the ratio of the base areas of cone and cylinder under certain constraints?
A cone and a cylinder have the same height, the same total surface area, and the same volume. What is the ratio of the area of the cone’s base to the area of the cylinder’s base?

Beste Antwort:

Answer by Stephen
3 : 1

Volume of cylinder: Ah (A=area of base; h=height)
Volume of cone: 1/3*Bh (B=area of base)

Ah = 1/3*Bh (The two figures have the same volume)

Because the solids have the same height, the h can be stricken from the problem:

A = 1/3*B

Now solve for B/A (the ratio of the area of the cone’s base to that of the cylinder):

B/A = 3/1 (hence the ratio 3:1)

I realize this doesn’t account for the surface area, but the surface area of a cone depends on a bit more (the slant height). The slant height, however, can be adjusted until the surface areas become the same, so it doesn’t need to be considered.

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