Error of Measurement?

Question

The radius of a circle is given as 10cm, with a possible error of measurement equal to 1mm. Use differentials to estimate the maximum error in the area, in cm^2

Answer 1

OK, so you're not sure of the radius. It can be anything from 9.9cm to 10.1cm.

The area of a circle is, of course, pi times the square of the radius. What you need to do is figure out pi*(10.1)^2, then figure out pi*(9.9)^2, and then figure out what the difference is between the two.

I'll let you plug in the numbers in a calculator yourself.

Answer 2

The smallest the radius could be is 9.9 cm, which would correspond to an area of 307.907496 cm^2.

The largest the radius could be is 10.1 cm, which would correspond to an area of 320.4738666 cm^2.

The maximum error in the area would be the difference between these two: pi*(10.1^2 - 9.9^2) = 12.56637061 cm^2.

Answer 3

you may could understand how precise your measuring gadget is. as an instance, if you're utilising a ruler, i'm guessing it can be precise to +/- 0.5mm. that signifies that each and each measurement could be incorrect by technique of 0.5 a millimetre. So... Take your first measurement of fifty cm. in the adventure that your ruler causes you to operate on or subtract 0.5 mm, your measurement could determination between 499.5 mm and 500.5 mm. So the percentage distinction is (0.5 / 500)*100 = 0.a million% blunders. in case you prepare that calculation to the smaller measurements, you'll discover that the percentage blunders will be higher because of the proportions.