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Hi there.
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So for this problem, for the first question in here, we are asked to find the surface of the earth in miles.
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Now, we note that the surface area, let's call that s, is equal to for a sphere, is four times pi times the radios of that sphere to the square.
00:24
Now, we know that the earth is, we can model the earth as a sphere, and then the radius of the earth in miles is equal to is given, and that is equal to 3 ,958 miles.
00:57
Miles.
01:01
So we just need to simply substitute that value into the expression for the surface area.
01:05
So the surface area is four times pi times that radios to the square.
01:16
So using our calculator, we obtain a value of 1 .97 times 10 to the mind to this, sorry, to the 8.
01:42
Square miles.
01:44
So that's a solution for part one of this problem.
01:48
Now for the second question in here, we are asked about that isn't the formula for the surface area.
01:57
We need to find the rate of change of the area and interpreted what it means.
02:03
So what we need to calculate is the derivative of the surface area with respect to the radius.
02:08
So that will be the derivative with respect to the radius...