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The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is __________.
Solution :
Volume of sphere :
$$V = \frac{4}{3}\pi r^3$$
Since diameter $$d = 2r$$,
$$V \propto d^3$$
Therefore,
$$\frac{\Delta V}{V} = 3\frac{\Delta d}{d}$$
Given percentage error in diameter :
$$\frac{\Delta d}{d} \times 100 = 2\%$$
Hence,
$$\frac{\Delta V}{V} \times 100 = 3 \times 2\%$$
$$= 6\%$$
Final Answer :
$$6\%$$
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