Question

The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm.

Answer 1

Answer:

a) $\Delta A \approx 26.389\,cm^{2}$, b) $r_{A} \approx 0.019$, c) $\delta = 1.9\,\%$

Step-by-step explanation:

a) The area of the circular disk is modelled after this expression:

$A = \pi \cdot r^{2}$

The total differential is given by the following formula:

$\Delta A = 2\pi r \cdot \Delta r$

The maximum absolute error in the calculated area of the disk is:

$\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)$

$\Delta A \approx 26.389\,cm^{2}$

b) The relative error is given by:

$r_{A} = \frac{\Delta A}{A}$

$r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}$

$r_{A} \approx 0.019$

c) The percentage error is:

$\delta = r_{A}\times 100\,\%$

$\delta = 0.019 \times 100\,\%$

$\delta = 1.9\,\%$