What is the possible error in the area of a circle if the radius is 10 cm with a possible error of 1 mm?

Answer 1

Start by finding the lowest possible area.... 10cm x 1000 = 10000mm (10cm = 10000mm) 100000 - 1 = 9999 (lowest possible area) Substitue this new radius into the area formula a=Ï€r2a=Ï€ x 99992 a =Ï€ x 99980001 a=314096436.64750018157128832392293 (This is the lowest possible area) Now find out the area of the circle with a radius of exactly 10cm (10000mm) a2 =Ï€r2 a2 =Ï€ x 100002 a2 =Ï€ x 100000000 a2=314159265.35897932384626433832795 (This is the area of a circle with a radius of 10cm) Now we can get our answer.... a2 - a = chance of error eithier way 314159265.35897932384626433832795 - 314096436.64750018157128832392293 = 62828.711479142274976014405 mm The above number is your margin of error from 10cm eithier way. Therfore the total chance of error (lowest possible to highest possible) is equal to the above number times 2.... 62828.711479142274976014405 x 2 = 125657.42295828454995202881 mm