A Rope Around the World
Imagine you have a rope tied tightly around the circumference of the world with no gap (imagine the earth is a perfect sphere). You then make this 1 metre longer and raise it away from the world evenly.
How big is the gap between the world and the rope?
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1 solution
The formula for the circumference of a circle (this is the same for the circumference of a sphere) is 2πr and therefore r = C/2π. Δr = ΔC/2π = (C+1m)/2π - C/2π = C/2π + 1/2π - C/2π = 1/2π m. 1/2π is 0.1591549 m = 15.9cm (3 s.f.)