shells: (A) The method of cylindrical shells: The circumference of a typical shell = The volume V = : So Therefore V= (B) The method of slicing from Sec(7.2): So The volume V = by rotating about the y-axis the region bounded by y = 72 and y = 3². Find V both by slicing and by cylindical Thus the volume V= and the height of this shell = da, where a = dy, where a = and b= and b=

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Let V be the volume of the solid S obtained by rotating about the y-axis the region bounded by y = √72x and y = 3x². Find V both by slicing and by cylindical
shells:
(A) The method of cylindrical shells:
The circumference of a typical shell =
The volume V=
Therefore V=
So
(B) The method of slicing from Sec(7.2):
The volume V = So
Thus the volume V =
and the height of this shell =
da, where a =
dy, where a =
and b =
and b =
Transcribed Image Text:Let V be the volume of the solid S obtained by rotating about the y-axis the region bounded by y = √72x and y = 3x². Find V both by slicing and by cylindical shells: (A) The method of cylindrical shells: The circumference of a typical shell = The volume V= Therefore V= So (B) The method of slicing from Sec(7.2): The volume V = So Thus the volume V = and the height of this shell = da, where a = dy, where a = and b = and b =
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