Question

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

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Answer 1

Dear student,

The volume of sphere is $V=\frac{4}{3}\pi r^3$

Taking log on both side
$$\begin{gathered} \log V=\log \frac{4}{3}+3\log R \\ Diffrentiatingonbothsides \\ \frac{∆V}{V}=0+3\frac{∆R}{R} \\ \frac{∆R}{R}=0.02\% \\ Then\frac{∆V}{V}=3\times 0.02=0.06\% \end{gathered}$$

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