If the error in the measurement of the radius | vedclass

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(C) The percentage error in the radius is given as $\frac{\Delta r}{r} 	imes 100 = 2\%$.The volume of a sphere is given by the formula $V = \frac{4}{

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$6$

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(C) The percentage error in the radius is given as $\frac{\Delta r}{r} 	imes 100 = 2\%$.The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Using the rules of propagation of errors for powers,the relative error in volume is $\frac{\Delta V}{V} = 3 	imes \frac{\Delta r}{r}$.To find the percentage error,multiply both sides by $100$:$\frac{\Delta V}{V} 	imes 100 = 3 	imes (\frac{\Delta r}{r} 	imes 100)$.Substituting the given value:$\frac{\Delta V}{V} 	imes 100 = 3 	imes 2\% = 6\%$.

If the error in the measurement of the radius of a sphere is $2\%$,then the error in the determination of the volume of the sphere will be ........ $\%$

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