Solution Found!
Constant volume tori The volume of a solid torus is given
Chapter 11, Problem 55E(choose chapter or problem)
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?
Questions & Answers
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