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Volume of a quarter cylinder between 2 planes

  1. Mar 26, 2015 #1

    Matternot

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    1. The problem statement, all variables and given/known data
    Find the volume V of the region that lies inside the quarter cylinder
    0 ≤ r ≤ 1, 0 ≤ θ ⇐ 1/2 π and between the planes x+y+z=4 and z=0, where (r, θ, z) are cylindrical polar coordinates.

    2. Relevant equations
    integral dV = integral r drdθdz

    3. The attempt at a solution
    I considered 4pi (volume of cylinder up to z=4) and the volume between the planes z=0 and x+y+z = 0

    My biggest problem is working out which I should take as my final variable to integrate. I assume it'll be r
     
  2. jcsd
  3. Mar 26, 2015 #2

    Matternot

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    Oops... Came up with a solution leading to the result π-2/3 immediately after posting. If anyone wants to check my answer, be my guest.
     
    Last edited: Mar 26, 2015
  4. Mar 27, 2015 #3

    haruspex

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    Looks right.
     
  5. Mar 27, 2015 #4

    Matternot

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    Thanks
     
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