Results 1 to 2 of 2

Math Help - surface area

  1. #1
    Newbie reddy9's Avatar
    Joined
    May 2008
    Posts
    5

    surface area

    A quick question:

    Cans of soup are often packed in boxes with spaces in between. Calculate the area that is wasted in between all the cans.

    The length is 24 cm and the width is 18 cm.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    You didn't mention what the radius of the circle of each can was so let's just call it r. I'm assuming we're looking from an overhead point of view and we're just focusing on the area of the 2-D plane created by the circles of the cans and the rectangle of the box.

    If the cans are positioned and aligned perfectly, the length of the rectangle should equal to the sums of the diameters of each can running along the length. So, if the radius of the circles is equal to r, then the diamater of each circle is 2r.

    The number of cans that can fit along the length is \frac{24 cm}{2r cm} = \frac{12}{r} (for example, if the diameter of each circle was 12 cm, then you can only fit 24/12 = 2 cans across the length of the box).

    Similar reasoning shows that there'll be \frac{18}{2r} = \frac{9}{r} cans along the width of the box.

    So, looking at the entire box, you'll see that there'll be \frac{9}{r} \times \frac{12}{r} circles, each with an area of \pi r^{2}. So you can find the summed area made by the cans and subtract it from the area of the rectangle created by the box.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Surface Area of Surface
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 1st 2010, 09:53 AM
  2. Calculate the surface area of the surface
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 26th 2009, 04:03 AM
  3. Lateral Area and Total Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 25th 2009, 04:28 PM
  4. Help finding surface area of a surface
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 3rd 2008, 04:11 PM
  5. Volume, Surface Area, and Lateral Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 14th 2008, 11:40 PM

Search Tags


/mathhelpforum @mathhelpforum