Question

The error in measurement of radius of sphere is $1$%, then estimated error in calculation of its volume will be:

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is B $3$

Error in measurement in radius $\frac{\Delta r}{r}\times 100=1$ %

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

Error in volume $\frac{\Delta V}{V}\times 100=3\frac{\Delta r}{r}\times 100$

$⟹\frac{\Delta V}{V}\times 100=3\times 1=3$ %