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

Answer: (D)

Given, error in diameter $=\pm 0.04$
$\therefore$ Error in radius, $dr=\pm 0.02$
$\therefore$ Per cent error in the volume of sphere
$=\frac{dV}{V}\times 100=\frac{d\left(\frac{4}{3}\pi r^3\right)}{\frac{4}{3}\pi r^3}\times 100$
$=\frac{3dr}{r}\times 100$
$=\frac{3\times (\pm 0.02)}{10}\times 100=\pm 0.6$