If the error in the measurement of the surfac | vedclass

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(B) The surface area $S$ of a sphere is given by $S = 4\pi r^2$,where $r$ is the radius.The relative error in surface area is given by $\frac{\Delta S

Vedclass · Accepted Answer

$1.8$

Vedclass · Answer

(B) The surface area $S$ of a sphere is given by $S = 4\pi r^2$,where $r$ is the radius.The relative error in surface area is given by $\frac{\Delta S}{S} = 2 \frac{\Delta r}{r}$.Given $\frac{\Delta S}{S} 	imes 100 = 1.2 \%$,we have $2 \frac{\Delta r}{r} 	imes 100 = 1.2 \%$,which implies $\frac{\Delta r}{r} 	imes 100 = 0.6 \%$.The volume $V$ of a sphere is given by $V = \frac{4}{3}\pi r^3$.The relative error in volume is given by $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$.Substituting the value of $\frac{\Delta r}{r}$,we get $\frac{\Delta V}{V} 	imes 100 = 3 	imes 0.6 \% = 1.8 \%$.

If the error in the measurement of the surface area of a sphere is $1.2 \%$,then the error in the determination of the volume of the sphere is (in $\%$)

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$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$.
$Reason$ : The permissible error is calculated by the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.

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