# Approximate error in circumference.

• Apr 16th 2010, 04:19 AM
dearppl
Approximate error in circumference.
A ball company manufactures many round sports balls, in order to fit the right number of balls into each box, their volume can vary by at most 1%. How accurately must the circumference be measured to ensure each box contains the right number of balls?

I know the answer is 1/3, but cant seem to get it right

Thanks guys!!
• Apr 16th 2010, 04:34 AM
mr fantastic
Quote:

Originally Posted by dearppl
A ball company manufactures many round sports balls, in order to fit the right number of balls into each box, their volume can vary by at most 1%. How accurately must the circumference be measured to ensure each box contains the right number of balls?

I know the answer is 1/3, but cant seem to get it right

Thanks guys!!

$\displaystyle V = \frac{4}{3} \pi r^3$. Therefore:

$\displaystyle C = 2 \pi r \Rightarrow C^3 = 8 \pi r^3 = 6V \Rightarrow C = (6V)^{1/3}$.

Now apply the linear approaximation.
• Apr 16th 2010, 04:52 AM
dearppl
sorry i am not quite sure where you are getting to, can you please explain more and the further steps thank you!
• Apr 16th 2010, 04:56 AM
mr fantastic
Quote:

Originally Posted by dearppl
sorry i am not quite sure where you are getting to, can you please explain more and the further steps thank you!

Go back and review linear approximation in your class notes or textbook. Then read my reply again. Please be specific if, after doing this, you still need help.