Question

The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is _________ % . (round off to two decimal places).

Hint:

When the quantity depends on the square of a measured value, the percentage error in the result is twice the percentage error in the measured value.

Answer 1

Correct Answer: 0.39

The area of the rod \( A \) is given by:
\[ A = \pi r^2 \] The error in the computed area is related to the error in the radius. The percentage error in area is twice the percentage error in radius. This is because the area depends on the square of the radius:
\[ \text{Percentage error in area} = 2 \times \text{Percentage error in radius} \] Given that the percentage error in radius is 0.2%, the percentage error in area is:
\[ \text{Percentage error in area} = 2 \times 0.2 = 0.4% \] Thus, the absolute percentage error in the computed area is:
\[ \boxed{0.40%} \]