Thread: 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

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

Sub those into the formula for circumference.

You get,

and

.

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

Solve for 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.

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.





The error in C is at most 2 cm so





The error in V would be dV





so

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