The circumference of a sphere was measured to be 75 cm with a possible error of 0.8 cm?

Question

Use differentials to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area..
The circumference of a sphere of radius r is c=2(pi)r, and its surface area is A=4(pi)(r^2). Eliminate r first! I did eliminat r from crcumference and then found derivative , but the answer is not what i am geting. PLease help

Answer 1

Arner, the ratio of area to circumference is
c = 2*pi*r, so r=c/2*pi so A = 4*pi*c^2 / (4*pi^2) = c^2/pi

So that dA / dc = 2c/pi

Now f(b) = f(a) + (b-a)*f'(a)

so the difference in area must be f(b)-f(a) = (b-a)*f'(a) = 0.8*2*0.75 / pi = 38.4 cm^2.

the real answer is 38.197

Comment - You don't say whether the 0.8 is the single sided error or the double sided so the answer could be +/- 38.4 cm^2 (single sided error) or +/- 19.2cm^2 (double sided).

hth

Answer 2

c = 2πr → r = c/(2π) Putting this in A,

A = 4π[c/(2π)]² = c²/π

Then dA = (dA/dc) dc = ((2c)/π) dc

When c = 75 and dc = 0.8, dA = (2)(75)(0.8)/π = 120/π

Answer 3

I would help u but i don't get math! Math teases my brain!