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?

AdminMod2
Aug 19, 2017

#1**+1 **

True area = pi (20/2)^2 = 100 pi cm^2

If he * underestimates *the circumference by 20%....the measured diameter is 20 * .80 = 16 cm

And the area in this case = pi (16/2)^2 = pi * 8^2 = 64 pi

So.....the percent error in the area in this case = l 100 pi - 64pi l / l 100 pi l = 36 / 100 = 36%

If he * overestimates *the circumference by 20%....the measured diameter = 20 * 1.20 = 24 cm

And the area in this case = pi (24/2)^2 = pi * 12^2 = 144 pi

So.....the percent error in this case = l 144 pi - 100 pi l / l 100 pi l = 44 / 100 = 44%

CPhill
Aug 19, 2017