# Thread: Juan and his spherical ball

1. ## Juan and his spherical ball

Need some help with the following question

Juan measures the circumference C of a spherical ball at 20 cm and computes the ball's volume V. Estimate the maximum possible error in V if the error in C is at most 2 cm. Recall that C = 2πr and V = (4/3)πr3, where r is the ball's radius. Give your answer correct to the nearest whole number.

Thank you

2. Ok. Maximum of C is 22, minimum is 18.

Sub those into the formula for circumference.

You get,

$\displaystyle 18 = 2 \pi r$ and

$\displaystyle 22 = 2 \pi r$.

These will give you the maximum and minimum radii he could have had.

Solve for $\displaystyle r$ in both cases and sub that into the formula for volume. You'll get a maximum and minimum volume. Find which one is farthest from the volume obtained by setting C=20 and find out how far. That is the largest error.

3. Originally Posted by elexis10
Need some help with the following question

Juan measures the circumference C of a spherical ball at 20 cm and computes the ball's volume V. Estimate the maximum possible error in V if the error in C is at most 2 cm. Recall that C = 2πr and V = (4/3)πr3, where r is the ball's radius. Give your answer correct to the nearest whole number.

Thank you
You could use differentials to estimate the error.

$\displaystyle C=2\pi r$

$\displaystyle dC=2\pi\,dr$

The error in C is at most 2 cm so

$\displaystyle 2=2\pi\,dr$

$\displaystyle dr=\frac{1}{\pi}$

The error in V would be dV

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

$\displaystyle dV=4\pi r^2\,dr$

$\displaystyle C=20$ so $\displaystyle r=\frac{10}{\pi}$

$\displaystyle dV=4\pi (\frac{10}{\pi})^2(\frac{1}{\pi})$

4. thank you guys very much, i got the correct answer and i understand it much more thoroughly, once again thank you