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A decorative oak post is 30 inches long and is turned on a lathe so that its profile is sinusoidal as shown in the figure below.

A decorative oak post is 30 inches long and is turned on a lathe so that its profile is sinusoidal as shown in the figure below.

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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A decorative oak post is 30 inches long and is turned on a lathe so that its profile is sinusoidal as shown in the figure below. y(s, t) = 1 + cos In this figure, ro = 4 inches and ag = 10 inches. (a) Describe the surface of the post parametrically using cylindrical coordinates and the parameters s and t. x(s, t) = 1 + cos 5)COS (1) z(s, t) = s, where 08≤ 30 and 0 ≤t≤ 2π = ST sin (t), and 2 (b) Find the volume of the post. volume = ? (Include units.) To ao
Transcribed Image Text:A decorative oak post is 30 inches long and is turned on a lathe so that its profile is sinusoidal as shown in the figure below. y(s, t) = 1 + cos In this figure, ro = 4 inches and ag = 10 inches. (a) Describe the surface of the post parametrically using cylindrical coordinates and the parameters s and t. x(s, t) = 1 + cos 5)COS (1) z(s, t) = s, where 08≤ 30 and 0 ≤t≤ 2π = ST sin (t), and 2 (b) Find the volume of the post. volume = ? (Include units.) To ao
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