Question

There is an error of $\pm$ 0.04cm in the measurement of the diameter of a sphere. When the radius is 10cm,the percentage error in the volume of the sphere is

• A. $\pm 1.2$
• B. $\pm 1.0$
• C. $\pm 0.8$
• D. $\pm 0.6$

Answer 1

The correct option is D

$\pm 0.6$

$\Delta d=\pm 0.04\Rightarrow \Delta r=\pm 0.02R=10cmV=\frac{4}{3}\pi r^3\frac{\Delta V}{V}\times 100=3\times \frac{\Delta r}{r}\times 100\frac{\Delta V}{V}\times 100=\pm 0.6$