Use disk method to find the volume of the solid obtained when the region bounded by the curve y= cos x, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use disk method to find the volume of the solid obtained when the region bounded
by the curve y= cos x, 0<x<r/2, and the x- axis is rotated about the x-axis.
(a) shade the region on the graph below
(b) Find the radius.
2
3
4
5
(c) Find the cross-section area.
1
(d) Express the volume as an integral.
Do not evaluate the integral.
Transcribed Image Text:Use disk method to find the volume of the solid obtained when the region bounded by the curve y= cos x, 0<x<r/2, and the x- axis is rotated about the x-axis. (a) shade the region on the graph below (b) Find the radius. 2 3 4 5 (c) Find the cross-section area. 1 (d) Express the volume as an integral. Do not evaluate the integral.
Expert Solution
Step 1

Disc method is one among several methods that is used to find the volume of a region of rotation. If the cross sections of the region are circles, then it is possible to divide the entire region into discs. In disc method, the cross sectional area is multiplied with the thickness of the cross section, say dx, to obtain the volume. 

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