The percentage error in the calculated volume | vedclass

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(C) The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Since the diameter $D = 2r$, we can express the volume in terms of the diameter as $V

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$6$

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(C) The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Since the diameter $D = 2r$, we can express the volume in terms of the diameter as $V = \frac{4}{3} \pi (\frac{D}{2})^3 = \frac{\pi}{6} D^3$.Taking the logarithmic differentiation, we get $\frac{\Delta V}{V} = 3 \frac{\Delta D}{D}$.Given that the percentage error in the diameter measurement is $\frac{\Delta D}{D} 	imes 100 = 2\%$.Therefore, the percentage error in the volume is $\frac{\Delta V}{V} 	imes 100 = 3 	imes (\frac{\Delta D}{D} 	imes 100) = 3 	imes 2\% = 6\%$.

The percentage error in the calculated volume of a sphere, if there is $2\%$ error in its diameter measurement, is . . . . . . .

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