The question is: The radius of a circular disk is given as 22 cm with a maximum error in measurement of 0.4 cm. Use differentials to estimate the maximum possible error in the calculated area of the disk. I have determined the area to be 55.292cm^2 however when I input the value to calculate the percent error, I am getting an incorrect value. I have tried dA/A = 55.292/22cm but its not giving me the right value. Anyone help?

Question

anonymous · Answer

is there a diagram on how the circular disk looks like?

anonymous · Answer

the volume of a circle is V=pi*r^2 therefore we would have to use that formula. I have already determined the change in the area, the only thing is getting the percent error.

aum · Answer

$$
A = \pi r^2 \
\frac{dA}{dr} = 2\pi r \
\frac{\Delta A}{\Delta r} \approx  2\pi r \
\Delta A \approx 2\pi r * \Delta r \
r = 22; ~~~\Delta r = 0.4 \
\Delta A \approx 2\pi * 22 * 0.4 = 17.6\pi = 55.2920 \text{ cm}^2. \
$$

aum · Answer

Do they ask for the percent error or the maximum possible error?
The maximum possible error = 55.2920 cm^2 rounded to one decimal of 55.3 cm^2.

anonymous · Answer

asking for Maximum error.

aum · Answer

55.3

aum · Answer

Maximum possible error = 55.3 cm^2
Area of the circle = pi * r^2 = pi * (22)^2 = 1520.5 cm^2
Percent error = 55.3/1520.5 * 100 = 3.64%

But if they did not ask for percent error then don't use this answer.

anonymous · Answer

Thank you for your help!