1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Average height of a cone

  1. Apr 18, 2009 #1
    1. The problem statement, all variables and given/known data
    find the anverage heigh of z=sqrt(a^2-x^2-y^2) constricted by the cone x^2+y^2<=a^2
    in the xy plane

    2. Relevant equations
    Average Height =(1/area)*double integral of region of [z]drdpheta

    3. The attempt at a solution
    I really have no idea how to solve this problem can you please point me in the right direction
  2. jcsd
  3. Apr 18, 2009 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    How about converting your Cartesian functions over to cylindrical coordinates?
  4. Apr 20, 2009 #3
    converted the cartesian equations to polar and used the 1/area*double integral of region R [z]rdrdpheta. I am having much difficulty integrating r*sqrt(a^2-r^2). i tried a trig substitution but dont know how to finish from there. please help me!
  5. Apr 20, 2009 #4
    replace z in that "1/area*double integral of region R [z]rdrdpheta" you wrote by what it is equal to looking at the surface. then you can use polar coordinates.
  6. Apr 20, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper

    If it's any help, you aren't integrating over a cone, you are integrating over a hemisphere.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook