The largest possible error in the area of the circle is of 44%.
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:
[tex]A = \pi \times 10^2 = 100\pi[/tex]
With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:
[tex]A = \pi \times 12^2 = 144\pi[/tex]
The error is given by:
[tex]E = 144\pi - 100\pi = 44\pi[/tex]
The percent error is the error divided by the initial amount, multiplied by 100%, hence:
[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]
More can be learned about the area of a circle at https://brainly.com/question/17326298
#SPJ1
