Question

percentage uncertainty in area of circle if uncertainty in radius is 3% is ​

Answer 1

Answer:

You’ve got the area, no problem. When calculating propagated uncertainty, there are a few special rules you can use. Notice that in the equation you use for the area, we are multiplying one value with an error with another with an error (in saying “r2"). The rule for calculating the resulting error of z=x∗y

is as follows:

(δzz)2=(δxx)2+(δyy)2

Therefore,

(δ(r2)r2)2=(δ(r2)2.5∗109cm2)2=(δrr)2+(δrr)2=2(δrr)2=2((0.1∗104cm)2.8∗104cm)2

Solve this for δ(r2)

. Then, use A=πr2⟹δA=πδ(r2) to solve for the uncertainty in