Question

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 1

The largest possible error in the area of the circle is of 44%.

What is the area of a circle?

The area of a circle of radius r is given by:

$A = \pi r^2$

With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:

$A = \pi \times 10^2 = 100\pi$

With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:

$A = \pi \times 12^2 = 144\pi$

The error is given by:

$E = 144\pi - 100\pi = 44\pi$

The percent error is the error divided by the initial amount, multiplied by 100%, hence:

$P = \frac{44\pi}{100\pi} \times 100\% = 44\%$

More can be learned about the area of a circle at brainly.com/question/17326298

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