The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches. (Use differentials to approximate the possible propagated error and the percent error.

Question

Propagated error= 1.6%

Percent error= 4.6%

Answer 1

the propagated error (dC) is 2π*dr = 1.57 inches, not 1.57%

the % error (dC/C) = .25/16 = 1.57%

Since circumference is a linear function of radius, its % error cannot be greater than the % error in the radius.