Question

The radius of a sphere is measured as $(10\pm 0.02\%)$ cm. The error in the measurement of its volume is

• A. $25.1$ cc
• B. $25.12$ cc
• C. $2.51$ cc
• D. $251.2$ cc

Answer 1

The correct option is B $25.12$ cc

Given,

$r=10\pm 0.02$%

Volume, $V=\frac{4}{3}\pi r^3$. . . . . . . . .(1)

$\frac{\Delta V}{V}=3\frac{\Delta r}{r}$

$\Delta V=3V\frac{\Delta r}{r}$

$\Delta V=\frac{4}{3}\pi r^3\times 3\times \frac{\Delta r}{r}$

$\Delta V=\frac{4}{3}\times 3.14\times 10\times 10\times 10\times 3\times \frac{0.02}{10}=25.12cc$

The correct option is B.