Results 1 to 3 of 3

Math Help - practical problem

  1. #1
    Jan 2010

    practical problem

    Hi there,

    Can anyone solve, or help me to solve a practical problem that I have.
    I have a rectangle which is 400mm by 300mm, I need to pack 40 equal circles of diameter 45mm onto this rectangle. I need to maximise the minimum distance between the circles. Another way of putting this is to say that I want the 40 circles to be as far away from each other as possible but still fit into my rectangle. Can anyone help with this?


    Last edited by Frankiejw; January 26th 2010 at 04:32 PM. Reason: error
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Sep 2008
    As your rectangle is fixed you should find the radius of your circles to detemine how many will fit. The sum of radii both longways and up and down will give you a length and width

    r= \frac{45}{2\pi}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Dec 2007
    Ottawa, Canada
    Place 8 along the 400 length: do this 5 times; that'll be total of 40 circles;
    so you have 5 rows of 8 circles.
    Stick the "outermost" 22 circles tangent to the rectangle's perimeter, with
    the 4 in the corners tabgent to 2 of the sides.

    8 * 45 = 360 ; 400 - 360 = 40 ; leave 40/7 as horizontal length in between circles.

    5 * 45 = 225 ; 300 - 225 = 75 ; leave 75/4 as vertical length in between circles.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Practical problem concerning expected value
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 27th 2011, 01:39 PM
  2. Practical problem
    Posted in the Algebra Forum
    Replies: 20
    Last Post: September 6th 2011, 08:05 AM
  3. practical differential problem
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 8th 2009, 08:50 AM
  4. Practical math problem...sort of a puzzle
    Posted in the Math Challenge Problems Forum
    Replies: 0
    Last Post: April 15th 2008, 04:27 PM
  5. Practical Optimization Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2007, 05:18 AM

Search Tags

/mathhelpforum @mathhelpforum