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. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

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.