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# Areo of circle

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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?

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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
edited by CPhill  Aug 19, 2017

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