Can you crawl under it?

Geometry Level 3

A length of wire completely surrounds the earth at the Equator. Imagine that the wire floats, that it has negligible mass, and that it fits snugly around the earth. Cut the wire and splice in an extra 20 feet of wire. Now the wire will be slightly slack in its fit. Raise the wire equally at all points away from the earth until it is tight again. A. How high will the wire be off the earth at all points?(Answer correct to 3 decimal points)


The answer is 3.183.

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3 solutions

Kunal Joshi
Apr 13, 2014

Let radius of earth be r . So intial length of wire = 2 π r 2 \pi r . Now 20 feet wire is added so circumference will increase, so let increased radius be R . Hence, 2 π r 2\pi r + 20 = 2 π R 2\pi R . So we get, R - r = 10 π \frac{10}{ \pi } . But, R - r is increased height. So we get, R - r = 3.1830988 \boxed{3.1830988}

Vivek Sedani
Apr 14, 2014

2piR1 + 20 = 2piR2 ; R2 - R1 = 20/(2pi) = 3.1830988

Guiseppi Butel
Apr 13, 2014

Change of R= R2- R1;

R1 = C1/2*pi,

R2= C2/2*pi;

C2= C1 + 20;

Change of R = 20/2*pi = 3.183

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