Question

The error in the measurement of radius of sphere is $0.3$%, what is percentage error in the measurement of its volume?

• A. $0.3$%
• B. $0.6$%
• C. $0.9$%
• D. $\frac{4}{3}\pi {\left(0.3\right)}^3$

Answer 1

The correct option is C $0.9$%

Error in radius, $\frac{\Delta r}{r}=0.3$%

Volume of sphere $=\frac{4}{3}\pi r^3$

$\therefore$ Error in volume $=3\times \frac{\Delta r}{r}$

$=(3\times 0.3)$ %$=0.9$%