Question:
If the percentage error in the radius of a circle is 3, then the percentage error in its area is:
If the percentage error in the radius of a circle is 3, then the percentage error in its area is:
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For percentage errors in power functions, multiply the error in the variable by the exponent.
Updated On: Mar 24, 2025
- \( 6 \)
- \( \frac{3}{2} \)
- \( 2 \)
- \( 4 \)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding percentage error propagation
The area of a circle is given by:
\[
A = \pi r^2.
\]
Differentiating both sides:
\[
\frac{dA}{A} = 2 \frac{dr}{r}.
\]
Multiplying by 100 to convert to percentage error:
\[
% { error in } A = 2 \times (% { error in } r).
\]
Step 2: Substituting given values
Given \(% \) error in \( r = 3 \):
\[
% { error in } A = 2 \times 3 = 6.
\]
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