- #1
Koranzite
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Homework Statement
A sphere of radius R with centre at the origin is cut by two parallel planes at [itex]z=\pm a[/itex], where a<R. Write, in cylindrical coordinates, a triple integral which gives the volume of that part of the sphere between the two planes. Evaluate the volume by first performing the r,θ integrals and the the remaining z integral.
Homework Equations
[itex] dV=rdrdθdz [/itex]
The Attempt at a Solution
The main probelm here is the setting up of my integral, as the answer I am getting is independant of R, which is then clearly wrong.
My integral runs from:
[itex]r=\sqrt{R^2-a^2}[/itex] to [itex] r=\sqrt{R^2-z^2} [/itex]
[itex] θ=0 [/itex] to [itex] θ=2\pi [/itex]
[itex] z=-a [/itex] to [itex] z=a [/itex]
I would expect the answer to depend on R, but it keeps cancelling out when I evaluate the r integral. I would be grateful if someone could explain what is wrong with my limits.