SOLUTION: In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to 20%.

Question 1190492: In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to 20%. What is the largest possible percent error, in percent, in Juan's computed area of the circle?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the error is + 20%, then he measures the diameter as 24.
if the error is - 20%, then he measures the diameter as 16.
if he is 0%, then he measures the diameter as 20.

the radius is half the diameters, so the radius can be 8, or 10, or 12.

the area of the circle is equal to pi * r^2.

the area can therefore be 64 * pi, or 100 * pi, or 144 * pi.

the correct area is 100 * pi.

if the area measures 64 * pi, then the error is 100 * pi - 64 * pi = 38 * pi.
38 * pi / (100 * pi) is an error of 38%.

if the area measures 144 * pi, then the error is 144 * pi - 100 * pi = 44 * pi.
44 * pi / (100 * pi) is an error of 44%.

it looks like the largest possible error in determining the area of the circle will be 44%.

let me know if you have any questions.

theo

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