Changes in torus surface area The surface area of a torus with an inner radius r and an outer radius R > r is S = 4π2(R2– r2).
a. If r increases and R decreases, does S increase or decrease, or is it impossible to say?
b. If r increases and R increases, does S increase or decrease, or is it impossible to say?
c. Estimate the change in the surface area of the torus when r changes from r = 3.00 to r = 3.05 and R changes from R = 5.50 to R = 5.65.
d. Estimate the change in the surface area of the torus when r changes from r = 3.00 to r = 2.95 and R changes from R = 7.00 to R = 7.04.
e. Find the relationship between the changes in r and R that leaves the surface area (approximately) unchanged.
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