Question

The road is 7m wide. The corner is in the shape of a quarter of a circle. the inside radius of the corner is 70m. Ali walks rounds the corner on the inside, from A to B. Obi walks round the corner on the outside, from C to D. How much further does obi walk than Ali?

Answer 1

No idea where A,B,C,D are, but let's just assume they are the ends of the 1/4 circle at the corner. Any distance along the straight portions will be the same for both people.

Since C=2πr for a whole circle, and we are only using a 1/4 circle, then the difference in distance between inner and outer circles is

π/2(R-r) = π/2*7 = 7π/2

If you want to do it the hard way, that is

π/2*(70+7) - π/2*70 = π/2(70+7-70) = 7π/2

All that matters is how wide the track is, not the radius of the circle.

Similarly, if you stretch a string around the earth, with a diameter of about 8000 miles (or some large number), if you then add 1 yard to the length of the string, it will rise off the ground by almost a foot! No matter how big the earth is.