Question

Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is:

• A. 1%
• B. 3%
• C. 5%
• D. 7%

Answer 1

Answer: (B)

3%

Answer 2

The volume of a sphere is given by $V = \frac{4}{3}\pi R^3$. The fractional error in volume is related to the fractional error in radius by $\frac{\Delta V}{V} = 3 \frac{\Delta R}{R}$. If the percentage error in radius is 1% ($\frac{\Delta R}{R} \times 100\% = 1\%$), then the percentage error in volume is $3 \times 1\% = 3\%$.