e method of cylíndrical shells to find the volume V

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) Use the method of cylindrical shells to find the volume V of the solid S obtained by rotating the region bounded by the given curves about the x-axis:
y = x° , x = 0, y = 27 ;
The circumference of a typical shell in terms of y = 2piy
The height of this shell in terms of y = 2piy^(4/3)
The volume V =
Sa 2piy^(4/3)
dy , where a =
and b =
27
Therefore V = 13122/7pi
(B) Use the method of slicing to find the volume V of the solid S:
The volume V =
dx , where a =
and b =
3
Thus the volume V = 2187/7pi
Transcribed Image Text:(A) Use the method of cylindrical shells to find the volume V of the solid S obtained by rotating the region bounded by the given curves about the x-axis: y = x° , x = 0, y = 27 ; The circumference of a typical shell in terms of y = 2piy The height of this shell in terms of y = 2piy^(4/3) The volume V = Sa 2piy^(4/3) dy , where a = and b = 27 Therefore V = 13122/7pi (B) Use the method of slicing to find the volume V of the solid S: The volume V = dx , where a = and b = 3 Thus the volume V = 2187/7pi
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