Assertion : The error in the measurement of r | vedclass

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(C) The surface area of a sphere is given by $A = 4\pi r^2$. Using the rules of error propagation,the relative error in $A$ is given by $\frac{\Delta

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If the Assertion is correct but Reason is incorrect.

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(C) The surface area of a sphere is given by $A = 4\pi r^2$. Using the rules of error propagation,the relative error in $A$ is given by $\frac{\Delta A}{A} = 2 \frac{\Delta r}{r}$. Given that the percentage error in the radius is $\frac{\Delta r}{r} 	imes 100 = 0.3\%$. Therefore,the percentage error in the surface area is $\frac{\Delta A}{A} 	imes 100 = 2 	imes (0.3\%) = 0.6\%$. Thus,the Assertion is correct. The Reason states the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$,which is incorrect because the correct relation is $\frac{\Delta A}{A} = 2 \frac{\Delta r}{r}$. Hence,the Assertion is correct but the Reason is incorrect.

$Assertion$ : 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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$Assertion$ : 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 $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.