00:01
Okay, we have a surface area problem.
00:04
So we need to parameterize the cone first.
00:06
So because it's, we have an x squared plus y squared, that's a circular behavior.
00:12
So we start with u, x equals u cosine v, y equals u sine v, and z is equal to 3u squared.
00:20
Okay? for z, when z is 3, plug that in, and then you'll see that u becomes 1, and when z is equal to 6, u becomes root 2.
00:30
So these are the boundaries of u and v.
00:34
V is the angle here.
00:36
So here's our r u v, and we need to find r u, which is derivative with respect to u, and r v with derivative with respect to v, and then do the cross product, and you get the cross product here, and then we need the magnitude of the cross product, which is right here.
00:52
Simplify it...