The diameter of a sphere is measured with a percentage error of 2%. What is the corresponding percentage error in the calculated volume of the sphere?
Options

Question

The diameter of a sphere is measured with a percentage error of 2%. What is the corresponding percentage error in the calculated volume of the sphere?

G1 Physics · Accepted Answer

For a sphere, V = (4 ÷ 3)πR³. Since the radius is proportional to the diameter, the percentage error in R is the same as the percentage error in the measured diameter: ΔR ÷ R = 2%. For V proportional to R³, ΔV ÷ V = 3(ΔR ÷ R). Therefore, percentage error in V = 3×2% = 6%. Correct option: C.