Calculus help!?

Question

A machinist is required to manufacture a circular metal disk with area 1700 cm2.

(a) What radius produces such a disk?
I found the answer to be 23.26 cm.

(b) If the machinist is allowed an error tolerance of ±6 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?

what's the answer to b? thanks so much!

Answer 1

The area of the circle is A = πr²

Then dA = 2 &pi r dr. Solve for dr.

dr = dA / 2 &pi r

You know dA = ±6 and you know r = 23.26, so

dr = ±6 / 2 &pi 23.26 = ±6 / 146.15 = ± 0.041cm

and this is the allowable tolerance for the radius to get the required tolerance in the disk area