I have a question from Chapter 7.3 - Trigonometric Substitutions from the book C
ID: 3193581 • Letter: I
Question
I have a question from Chapter 7.3 - Trigonometric Substitutions from the book Calculus - Early Transcendals. 70. BAGEL WARS - Bob and Bruce bake bagels (shaped like tori). They both make standard bagels that have an inner radius of 0.5 in and an outer radius of 2.5 in. Bob plans to increase the volume of his bagels by decreasing the inner radius by 20% (leaving the outer radius unchanged). Bruce plans to increase the volume of his bagels by increasing the outer radius by 20% (leaving the inner radius unchanged). Whose new bagels will have the greater volume? Does this result depend on the size of the original bagels? Explain. I need the full steps, and full details. Thanks.Explanation / Answer
V = 22Rr2
r = [2.5-0.5]/2 = 1 in
R = 0.5 + 1 = 1.5 in
V = 29.5788 in3
For Bob,
new inner radius = 0.5 - (0.5x0.2) = 0.49 in
r = [2.5-0.49]/2 = 1.005 in
R = 0.49 + 1.005 = 1.495 in
V = 29.7757 in3
For Bruce,
new inner radius = 2.5 + (2.5x0.2) = 3 in
r = [3-0.5]/2 = 1.25 in
R = 0.5 + 1.25 = 1.75 in
V = 53.92 in3
Bruce will have the larger bagel.
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