Finding the volume using double integralsFind 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).

Question

Finding the volume using double integralsFind 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&#039;t see how they are planes, are they planes or are they just lines in the zx plane (when   y  =  0).

lelapem · Accepted Answer

Explanation: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.

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

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