Question

The radius of a sphere is measured to be $(4.0+2.0)$ cm the maximum percentage error in the measurement of the volume of the sphere is

• A. $10$ %
• B. $15$ %
• C. $20$%
• D. $25$ %

Answer 1

The correct option is B $15$ %

Given,

$r=(4\pm 0.2)cm$

$\frac{\Delta r}{r}=\frac{0.20}{4}=0.05$

Volume, $V=\frac{4}{3}\pi r^3$

$\frac{\Delta V}{V}\times 100=3\frac{\Delta r}{r}\times 100=3\times 0.05\times 100=15$%

The correct option is B.