Answer to Question #451 in Algebra for Whitney

Question

With what accuracy should the length of the equator be measured to figure out the volume of the Earth with the accuracy of 1 km³ (If consider the Earth as the ideal sphere with the radius of 64000 km)?

Answer 1

Let r be the radius of the Earth. Then the length of the equator is L = 2πr. And the volume is V = (4/3)*πr³. Thus, we can define the volume through the length of the equator as V = L³/6π². Thus, if we need to measure this value with the accuracy of 1 km³ we should measure L with the accuracy of √3(6π²)km.