Question

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 $\frac{\Delta A }{ A }=\frac{4 \Delta r }{ r }$

• A. If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
• B. If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
• C. If the Assertion is correct but Reason is incorrect.
• D. If the Assertion is incorrect -and Reason is correct.

Answer 1

Answer: (C)

Area $A =4 \pi r^2$
Fractional error $\frac{\Delta A}{A}=\frac{2 \Delta r}{r}$
$\frac{\Delta A}{A} \times 100=2 \times 0.3 \%=0.6 \%$