Chapter 12.5, Problem 59E

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

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