Question

If the radius of a sphere is 50+-1....show
that the uncertainty of its volume is 6%

Answer 1

Answer:

V = 4/3 pi R^3

dV = 4 pi R^2    differential of V

dV / V = 3 dR / R = 3 * 1 / 50 = .06 = 6%

That assumes you have had calculus

If not then you need to expand (R + dR)^3 and

drop terms that contain dR^2 and dR^3 because they are small

that is [(R + dR)^3 - R^3] / R^3