Question

@rational

Answer 1

Let S be the part of the sphere \[x^2+y^2+z^2=25\] that lies above the plane z = 4. If S has the density k, find the center of mass.

Answer 2

I'm trying to get the mass, I'm using polar coordinates, but I don't exactly know what the intervals for r are.

Answer 3

Oh wait I figured it out, it's \[0 \le r \le 3\]

Answer 4

Yup :), thanks!

Answer 5

By symmetry the center of mass must lie on z axis

the exact height can be obtained by the formula
http://gyazo.com/f99245dff5c73b3ec8e327fde01b9f7c


you may use that for double checking..