Error Analysis: Practice Problem & Solution
Assertion (A): The error in measurement of radius of the sphere is 0.3%. The permissible error in its surface area is 1.2%. Reason (R): Area of sphere, \(A = 4\pi r^2 \Rightarrow \frac{\Delta A}{A} = 4\frac{\Delta r}{r}\).
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Error Analysis. Understanding the underlying formula is key to arriving at the correct answer below:
The surface area of a sphere is \(A = 4\pi r^2\), which gives the fractional error relation as \(\frac{\Delta A}{A} = 2\frac{\Delta r}{r}\). Thus, the error in area is \(2 \times 0.3% = 0.6%\), making both statements false.
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