Constant volume tori The volume of a solid torus is given

Chapter 11, Problem 55E

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QUESTION:

Constant volume tori The volume of a solid torus (a bagel or doughnut) is given by \(V=\left(\pi^{2} / 4\right)(R+r)(R-r)^{2}\), where r and R are the inner and outer radii and R >r (see figure).

a. If R and r increase at the same rate, does the volume of the torus increase, decrease, or remain constant?

b. If R and r decrease at the same rate, does the volume of the torus increase, decrease, or remain constant?

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QUESTION:

Constant volume tori The volume of a solid torus (a bagel or doughnut) is given by \(V=\left(\pi^{2} / 4\right)(R+r)(R-r)^{2}\), where r and R are the inner and outer radii and R >r (see figure).

a. If R and r increase at the same rate, does the volume of the torus increase, decrease, or remain constant?

b. If R and r decrease at the same rate, does the volume of the torus increase, decrease, or remain constant?

ANSWER:

Solution 55EStep 1:The volume of a solid torus is given by V = (2/4)(R + r)(R r)2, where r and R are the inner and outer radii and R > r

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