Find The Volume V Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified Line. 3x = Y2, X = 0, Y = 5; About The Y-Axis V =

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06-12-2022
Mathematics

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Find The Volume V Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified Line. 3x = Y2, X = 0, Y = 5; About The Y-Axis V =

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tutorconsortium401 tutorconsortium401 · Answer 1 · 2022-12-08T13:01:48-05:00

The Method of Cylindrical Shells will be used to assist.

What is Cylindrical Shells?

As previously, we construct a region R that is enclosed on the top by the graph of the function y = f (x), on the bottom by the x axis, and on the left and right by the lines x = a and x = b, respectively (a).

As seen in Figure 1, we then rotate this region around the y-axis (b). Be aware that this is distinct from what we have previously done..

Previously, areas that were described in terms of x-functions were centered on the x-axis or a line that ran parallel to it.

Since the shell is a cylinder, its volume equals the cross-sectional area times the cylinder's height. The cross-sections are annuli, which are essentially circles with holes in the middle and are formed like rings.

According to our question-

V= 2π ∫025/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units

USING THE WASHER METHOD

V = ∫05 π (1/4) y4 d y = 625π/ 4 cubic units

Hence, The Method of Cylindrical Shells will be used to assist.

Learn more about Cylindrical Shells click here:

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What is Cylindrical Shells?

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