SOLUTION: A person six feet tall walks around the earth. Assuming the earth is a perfect sphere, how many feet farther does the top of this person's head travel than the bottoms of his feet?

Question 1033442: A person six feet tall walks around the earth. Assuming the earth is a perfect sphere, how many feet farther does the top of this person's head travel than the bottoms of his feet? Express your answer in terms of $\pi$.
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
CIRCUMFERENCE, for radius r, ;
The difference in the path length traveled is

.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The circumference of a sphere is 2pi*r
The circumference of a sphere 6 feet wider is (2*pi*(r+6 feet))
The ratio is r+6 feet/r
If we use 4000 miles for the Earth's radius, the circumference is 2*pi*4000=8000*pi
The radius to the person's head, using 6 feet as 1/880 mile, is 2*pi*4000(1/880)=8000*(2/880)*pi
The difference is pi(8000 2/880)-8000=2pi/880 miles
This is 12 pi feet.
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