# Average height of a cone

## 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

quantumdude
Staff Emeritus
Gold Member
How about converting your Cartesian functions over to cylindrical coordinates?

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!

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.

Dick