math question

Question

The circumference of a sphere was measured to be 84 cm with a possible error in measurement of 0.5 cm. Use differential to estimate the maximum error in the calculated volume. What is the relative error?

Thank you

Answer 1

Hi Brooklyn,

To answer your first question, you need to use calculus to find the differential of a volume of a sphere.

The volume of a sphere is

V = 4/3*pi*r^3

If we differentiate with respect to r, then the rate of change becomes

V' = 4pir^2r'

Or, approximating with a differential:

change in V = 4pir^2(change in r).

You can use the above equation with the circumference (which will tell you r) and the difference in r to find the maximum error.

For the second part of the question, to find the relative error, you need:

(change in V)/V = 4pir^2(change in r)/4pir^3

You have all of the pieces and can plug in to find your answer. :)

Let me know if I can help you further. Good luck!