3550.44 – Walking the Equator

Sylvia McGibbins walks around the earth at the equator. She is 6' tall. How much further does her head travel than her feet? For amusement's sake, make a guess before working it out.

Solution

The circumference of a circle of radius $r$ is given by the formula $2\pi r$ . If $R$ is the radius of the earth (in feet), then Sylvia's feet walk $2\pi R$ feet while her head travels $2\pi (R + 6)$ feet. The difference is $2\pi 6$ feet, or $2\pi$ (about $6$ ) times Sylvia's height. Surprised? The result is independent of the radius of the earth. The same answer is correct if Sylvia walks around a bowling ball.