Results 1 to 4 of 4

Math Help - Juan and his spherical ball

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    21

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    Ok. Maximum of C is 22, minimum is 18.

    Sub those into the formula for circumference.

    You get,

    18 = 2 \pi r and

    22 = 2 \pi r.

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

    Solve for 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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2
    Quote Originally Posted by elexis10 View Post
    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.

    C=2\pi r

    dC=2\pi\,dr

    The error in C is at most 2 cm so

    2=2\pi\,dr

    dr=\frac{1}{\pi}

    The error in V would be dV

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

    dV=4\pi r^2\,dr

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

    dV=4\pi (\frac{10}{\pi})^2(\frac{1}{\pi})
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    Posts
    21
    thank you guys very much, i got the correct answer and i understand it much more thoroughly, once again thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume of a Ball
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 29th 2010, 01:53 AM
  2. linear map open iff image of unit ball contains ball around 0
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 25th 2010, 01:15 AM
  3. A ball is tossed...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 11th 2009, 04:53 PM
  4. Height of a ball
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 15th 2009, 06:20 PM
  5. Ball-bags
    Posted in the Statistics Forum
    Replies: 3
    Last Post: February 9th 2009, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum