00:01
Okay, so, um, what we're gonna do is we need to find this angle phi and it comes from the cone.
00:09
Okay, z is rho cosine of phi and squared of x squared plus y squared is rho sine of phi.
00:19
Rho cancels out.
00:21
So from here you get tangent of phi is equal to 1 over root 3 and that is 30 degrees, pi over 6, right? so phi is gonna run from 0 to pi over 6 and theta is gonna run all around because we have this projection over here, the circle, and rho is gonna run from 0 to 4.
00:52
Okay, nice, perfect.
00:56
0 to 2 pi, 0 to pi over 6 and 0 to 4, rho squared sine phi, d rho, d phi, d theta.
01:11
Break it apart like this.
01:18
Rho squared, d rho, and 0 to pi over 4, sine phi, d phi...