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Finding volume of a figure using the disk and washer method

label Calculus
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schedule 1 Day
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Find the volume of the figure with the parameters y=x y=2 and x=0 and rotate around the line y=3

Apr 16th, 2015

This is hard to describe without the use of a visual which I can't really use, but I will try my best. Basically you find the volume by finding the volume of a cylinder, then subtracting the inner cylinder part and taking half of the resulting volume. 

The first cylindrical volume that we want to figure out is has a circular base with a diameter of 6 and height of 2. The volume would be (pi)(3)^2 X 2 = 18(pi)

The cylinder to subtract from that has a base with diameter of 2 and height of 2. The volume would be (pi)(1)^2 X  2 = 2(pi)

When subtracting the volume, the resulting figure has a volume of 16(pi). You would then take half of that volume to figure out the volume of the 3D triangle formed since a triangle is half of a box.

Thus the volume of the figure we are looking for is 8(pi)

I hope this makes sense and you can visualize it or understand what I am saying. As said before, I can't really provide a visual.

Apr 16th, 2015

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Apr 16th, 2015
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Apr 16th, 2015
Jun 27th, 2017
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