Question 890733: the circular top of a coffee table is to have an area differing from 225 pi in^2 by less than 4 in^2. How accurately must the radius of the top be measured? delta is less than or equal to 0.1
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area can be as little as 221 and as large as 229.
to get an area larger than or equal to 221, the radius will have to be equal to the square root of 221 = 14.866068...
to get an area smaller than or equal to 229, the radius will have to be equal to the square root of 229 = 15.132745...
if we round to the nearest 10th of an inch, then the radius has to be greater than 14.9 and less than 15.1
you want to round on the high side for the smaller radius and round on the low side for the larger radius.
15 - 14.9 = .1
15.1 - 15 = .1
looks like .1 will do it if you want to measure to the nearest 10th of an inch.
when the radius is 14.9, the area will be 14.9^2 * pi = 222.01 * pi.
when the radius is 15.1, the area will be 15.1^2 * pi = 228.01 * pi.
if you want to get closer, you would round to the next highest hundredth of an inch on the low side and round down to the next highest hundredth of an inch on the high side.
you would get 14.86 on the low side.
you would get 15.13 on the low side.
note that the difference in radius on the low side and the high side are not the same anymore.
the low side difference is equal to 15 - 14.86 = .14
the high side difference is equal to 15.13 - 15 = .13
the reason for this is because the squaring effect on the larger radius is more than the squaring effect on the smaller radius.
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