00:01
Alright, so what we want to do is to graph the function first, or rewrite the equation to be, this would be x equal to the square root of 36 minus y squared.
00:14
And then finding our surface area, we'll have 2 pi from this would be negative 6 to 6.
00:22
This would be the square root of 36 minus y squared, and times the square root of 1 plus the derivative which is going to give us negative 2y over the square root of this would be 2 square root of 36 minus y squared and then squared and then this would be dy so simplifying this is 2 pi is negative 6 to 6 we're gonna have big big square root, we have 36 minus y squared times 1 plus 2 to cancel, this would be y squared over 36 minus y squared dy, so simplifying, it's 2 pi from negative 6 to 6 of this square root this would be of 36 minus y squared and then plus y squared so then these are just cancel and this is dy so this is 2 pi negative 6 to 6 of the square root of 36 which we just simplify to be 6 6 dy so therefore it becomes 2 pi times 3y squared from negative 6 to 6 2 pi times plug in an upper bound we'll get 3 times 36 which is going to give us 108 and then minus this would be 108 so in this case window with 0 so since we are equivalent in the denominator and and the numerator, then what we should do is change the bounds at this point to be two times two pi, because this is a semi -circle on both sides of the axis.
02:33
That's why i counted out.
02:34
Should be two times two pi, this from zero to six, oh six dy.
02:42
So we're gonna have four pi, this would be times three y squared, or three y actually...