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a. Find a formula for the volume Vof the cone in terms of x and a. h. Findrand h in the cone of maximum volume for a - 4, 5, 6, 8.

a. Find a formula for the volume Vof the cone in terms of x and a. h. Findrand h in the cone of maximum volume for a - 4, 5, 6, 8.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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61. Generalized cone problem A cone of height h and radius r is constructed from a flat, circular disk of radius a in. by removing a sector AOC of are length x in. and then connecting the edges OA and OC. a. Find a formula for the volume V of the cone in terms of x and a. b. Findrand h in the cone of maximum volume for a - 4,5, 6, 8. c. Find a simple relationship between r and h that is independent of a for the cone of maximum volume. Explain how you arrived at your relationship. NOT TO SCALE
Transcribed Image Text:61. Generalized cone problem A cone of height h and radius r is constructed from a flat, circular disk of radius a in. by removing a sector AOC of are length x in. and then connecting the edges OA and OC. a. Find a formula for the volume V of the cone in terms of x and a. b. Findrand h in the cone of maximum volume for a - 4,5, 6, 8. c. Find a simple relationship between r and h that is independent of a for the cone of maximum volume. Explain how you arrived at your relationship. NOT TO SCALE
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