Find the volume of the wedge sliced from the cylinder x^2+y^2=1 by the planes z=a(2-x) and z=a(x-2) a>0

Lillie Pittman 2022-07-17 Answered
Finding the volume using double integrals
Find the volume of the wedge sliced from the cylinder x 2 + y 2 = 1 by the planes z = a ( 2 x ) and z = a ( x 2 ).
I am confused because x 2 + y 2 = 1 is a unit circle not a cylinder. and the other two are lines in the zx plane where y = 0. I don't see how they are planes, are they planes or are they just lines in the zx plane (when y = 0).
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Answers (1)

Answered 2022-07-18 Author has 12 answers
In a figure showing the (x,z)-plane the two given planes appear as lines intersecting the x-axis at x = 2 and the z-axis at z = ± 2 a. Looking at the figure one realizes that because of symmetry the volume in question is 4 a π, whereby π stands for the area of the circle x 2 + y 2 1.

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