00:01
We're going to be painting a half dome hemisphere.
00:07
The radius is said to be 100 feet, but plus or minus six inches or half a foot.
00:16
So we have some tolerance here.
00:18
We don't know.
00:19
They didn't measure it exactly.
00:22
So what we want to figure out is, you know, given this tolerance, how much extra paint should be.
00:30
So the area of the hemisphere is 2 pi r squared.
00:33
The area of a sphere is 4 piar squared, so we're just half of that.
00:38
We're told the cost of a can of paint is $30.
00:43
So the cost is $30 per can.
00:46
And i just defined this row and it basically that how many square feet per can we can cover with the paint.
00:54
So we can cover 300 square feet of paint per can.
00:58
So we need to figure out how much this area may differ given the small, deviation here.
01:06
And so we can take the differential here and we get da equals 4 pi r dr, d .r, d .a, d .a equals, then, we can plug this stuff in.
01:20
So 4 pi r was the nominal value is 100, plus or minus one half.
01:27
And so that gives us plus or minus 628 square feet.
01:32
Now, if we're on the high side here, we need to make sure we have extra paint.
01:37
And so if we can only buy full cans of paint, we're going to need two.
01:41
Two won't cover it, but three will need three extra cans of paint.
01:46
And that will cost $90...