Question

Find the volume below the surface z=(sqrt(16-x^2-y^2)) which lies above the cone Z^2=3x^2+3y^2

Answer 1

First, set up your integral.

Answer 2

But before that shouldnt we turn the variables into polar?

Answer 3

I was thinking that was part of the setting up process. Go for it.

Answer 4

haha ok sorry. Lemme see....

Answer 5

z=sqrt(16-(rcostheta)^2-(rsintheta)^2
=sqrt(16-r^2)

Answer 6

z=-r+4

Answer 7

Good so far.

Answer 8

z^2=3(x^2+y^2)
z^2=3(r^2)

Answer 9

Substitute for z.

Answer 10

r=sqrt(8)

Answer 11

Hm, that's not what I got. Let me recheck.

Answer 12

Yeah, I didn't get sqrt(8). Check your math. One of us is wrong.

Answer 13

Wait what did you get?

Answer 14

i got r=2

Answer 15

@Mertsj please help