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 (Δ A / A )=(4 Δ r / r )

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 (Δ A / A )=(4 Δ 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.

Tardigrade Admin · Accepted Answer

Area A =4 π r2 Fractional error (Δ A/A)=(2 Δ r/r) (Δ A/A) × 100=2 × 0.3 %=0.6 %

Q. 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 $\frac{Δ A}{A} = \frac{4Δ r}{r}$

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

If the Assertion is correct but Reason is incorrect.

If the Assertion is incorrect -and Reason is correct.

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

Q. 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 AΔA​=r4Δr​