So we want to find the average value of a temperature function on a cone and the cone were given a Z squared equals X squared plus y squared where we know that Z is between zero and two. So for a temperature function of Z is equal to 100 minus 25 z. We know that the sphere in parametric form for a conical surfaces are equals our co sign Fada, our sign theta are, um and we know that our is between zero and two and theta is between zero and two pi. So we know that are part conservative arm is going to give us co sign theater sine theta one And then our parson narrative data is going to give us negative r sine theta negative r sine theta, then zero. And, um, we can expect this end of giving us, um when we crossed them. So our cross r theta we'll get a negative are because I'm theta negative. Our sign See you down are and then we take the magnitude of that We'll end up getting is just discriminative too are so now, um t equal to 100 minus 25 z we can write Z as are so have this double integral after i d s the surface in her room. I mean, what wind up getting as a result is 100 minus 25 r d s and this is gonna be from zero to to this will be from 0 to 2 pi and then instead of DS, it'll be, um, times the square root of two are d r d theta. So when we solve this further, obviously the Jew pie will just be off by itself, and then we'll multiply that by the rest of the in the room, which is going to be 1600 route to over six. So we end up getting is just a three. We get 1600 Route two pi over three. Um, also, when we do it with the cross product, So let me do it with this right here. What we're gonna end up getting is four route to pipe. So then, in order to get the average we take, um, the F average going to be the double in a girl service in the room FDs over the double integral DS. So what? That's gonna give us is 1600. Route two Pi over three, divided by four. Route to Hi. We see that the route to is getting cancel and the four will cancel giving us 400. The pie is gonna cancel. So our final answer is going to be 400 over three as our final answer.