maximum error?

Question

The circumference of a sphere was measured to be cm with a possible error of cm. Use differentials to estimate the maximum error in the calculated surface area.

Estimate the relative error in the calculated surface area.

Hint: The circumference of a sphere of radius r is , and its surface area is . Eliminate first!

Answer 1

S = 4pi*r^2
dS =8pir dr but 2pi*r is the circumference C
and
dC= 2pi dr
so dS =4r*dC =2/pi *C*dC