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Average height of a cone

  • Thread starter jimbo71
  • Start date
  • #1
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Homework Statement


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


Homework Equations


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


The Attempt at a Solution


I really have no idea how to solve this problem can you please point me in the right direction
 

Answers and Replies

  • #2
Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
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How about converting your Cartesian functions over to cylindrical coordinates?
 
  • #3
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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!
 
  • #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.
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
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If it's any help, you aren't integrating over a cone, you are integrating over a hemisphere.
 

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