Given:
The radius of the circular disk is 24cm.
The radius has a maximum error of 0.2 cm.
To find:
The area
Explanation:
Using the area of the circle,
[tex]A=\pi r^2[/tex]
The area of the disk is,
[tex]\begin{gathered} A=\pi\times24^2 \\ =576\pi cm^2 \end{gathered}[/tex]
If the radius is increased from 24 by 0.02, then the radius becomes, r = 0.02
The change in the calculated area will be,
[tex]\begin{gathered} \Delta A=Area\text{ of the cirlce with radius of 24.02-Area of the circle with radius of 24} \\ =\pi\times24.02^2-\pi\times24^2 \\ =576.96\pi-576\pi \\ =0.96\pi cm^2 \end{gathered}[/tex]
The relative percentage of area is,
[tex]\begin{gathered} \frac{\Delta A}{A}\times100=\frac{0.96\pi}{576\pi}\times100 \\ =0.0017\times100 \\ =0.17\text{ \%} \end{gathered}[/tex]
Final answer:
The maximum error in area is,
[tex]0.96\pi cm^2[/tex]
The relative percentage error in the area is 0.17%.
