00:01
Okay, the surface area of formula is the double integral of the square root of partial with respect to x squared plus the partial with respect to y squared plus 1, da.
00:13
So first we need to solve this for z.
00:18
So 64 minus x squared minus y squared to the one half.
00:25
Okay, so that's our function.
00:27
So i'm going to take the derivative with respect to x.
00:30
I get one half.
00:31
64 minus x squared minus y squared to the minus one half times minus two x and then zy will be exactly the same separate with a y to y so then z x squared plus zy squared plus one that will be x squared over 64 minus x squared minus y squared plus y squared over 64 minus x squared minus y squared plus one so x squared plus y squared plus 64 minus x squared minus y squared all over 64 minus x squared minus y squared so i got a common denominator there okay so those cancel so you get 64 over 64 minus x squared minus x squared minus y squared so i got a common denominator there okay so those cancel so then the arc length will be the double integral of the square root of that, da.
01:56
Okay, so now we're going to find da.
01:59
So we got to see what we got in the x and y plane.
02:03
So if i had a little flashlight up here and it's shining down, then what i will get is a circle.
02:14
Okay, and it's the circle where z equals 1 intersects z equals, 64 minus x squared minus y squared to the one half.
02:27
All right.
02:27
So 1 equals 64 minus x squared minus y squared or x squared plus y squared equals 63.
02:40
Okay, so it's a circle whose center is the square root of 63...