Solution Found!
Changes in torus surface area The surface area of a torus
Chapter 10, Problem 31E(choose chapter or problem)
Changes in torus surface area The surface area of a torus (an ideal bagel or doughnut) with an inner radius r and an outer radius \(R>r \text { is } S=4 \pi^{2}\left(R^{2}-r^{2}\right)\).
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.
Questions & Answers
QUESTION:
Changes in torus surface area The surface area of a torus (an ideal bagel or doughnut) with an inner radius r and an outer radius \(R>r \text { is } S=4 \pi^{2}\left(R^{2}-r^{2}\right)\).
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.
ANSWER:Solution 31E
Step 1 :
Given that The surface area of a torus with an inner radius r and an outer radius R > r is