The diameter of a shpere is measured to be 6 inches with a possible error of 0.05 inches. Use differentials to estimate the maximum error in the calculated surface area.

I've gotten this far:
A=4pir^2
dA=8(pi)(r)(dr)

Since the problem gives me the diameter and the equation A=4pir^2 uses the radius, do I divide both the radius and dr (.05) by two, giving me:
dA=8(pi)(3)(.025)
dA=1.88

1 answer

the error (in D) is ±.05

A = π D²

dA = 2 π D dD = .6 π

same difference...