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 \[\frac{\Delta A}{A}=\frac{4\Delta r}{r}\]

Options

• Assertion is True, Reason is True; Reason is a correct explanation for Assertion

• Assertion is True, Reason is True; Reason is not a correct explanation for Assertion

• Assertion is True, Reason is False

• Assertion is False, Reason is False.

Answer 1

Assertion is True, Reason is False

Explanation: 

\[\mathrm{A}=4\pi\mathrm{r}^2\]
\[\begin{aligned} & \text{Using Mindbenders}-2,4\pi\text{ being constant does} \\ & \text{not contribute to the error.} \\ & \text{Fractional error }\frac{\Delta\mathrm{A}}{\mathrm{A}}=\frac{2\Delta\mathrm{r}}{\mathrm{r}} \\ & \frac{\Delta\mathrm{A}}{\mathrm{A}}\times100=2\times0.3\%=0.6\% \end{aligned}\]