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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 $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
If the Assertion is correct but Reason is incorrect.
If both the Assertion and Reason are incorrect.
Solution
$\begin{array}{l}
Area\,of\,the\,sphere,\,A = 4\pi {r^2}\\
\% \,error\,in\,area\, = 2 \times \% \,error\,in\,radius\\
i.e,\,\frac{{\Delta A}}{A} \times 100 = 2 \times \frac{{\Delta r}}{r} \times 100\\
= 2 \times 0.3\% = 0.6\% \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,But\frac{{\Delta A}}{A} = 4\frac{{\Delta r}}{r}\,is\,false.
\end{array}$
