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 $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
Reason : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
AIIMS 2008, Easy
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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
$\%$ 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
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