Adding $2\pi$ inches to a string about the Earth's equator makes a new circle reaching how far above the ground?

Question

Sofia wraps a long string around the equator of the earth, pulling it snug. If the earth were a perfect sphere, the string would be touching the ground all along its length. Suddenly, Sofia stretches the string by 2π inches. If the looser string were now pulled taut into a circle above the equator, how many inches above the ground would it be, on the average?

I don't even know where to start with this.

How does the radius of a circle change if its circumference increases? — John Douma, Oct 28 '18 at 23:01

score 1 · Answer 1 · answered Oct 28 '18 at 23:03

1

Use $C_1 = 2 \pi r_1$ and $C_2 = (C_1 + 2 \pi) = 2 \pi r_2$, all measured in inches. Then compute $r_2 - r_1$.

answered Oct 28 '18 at 23:03

David G. Stork

29,774

score 0 · Accepted Answer · answered Oct 29 '18 at 05:13

$C_1= 2\pi r_1$ new circumference equals to $C_2 = (C_1 + 2 \pi) = 2 \pi r_2$ just as David has done then replace $C_1$ with $2\pi r_1$ so the equation becomes $2\pi r_1 + 2 \pi = 2 \pi r_2$ re arranging yeilds $2\pi = 2\pi(r_2 - r_1)$ the deviding both sides by $2\pi$ gets us $(r_2 - r_1) = 1 $ so the answer is 1 inch.

Adding $2\pi$ inches to a string about the Earth's equator makes a new circle reaching how far above the ground?

2 Answers2