Results 1 to 5 of 5

Math Help - Dimensional Analysis

  1. #1
    Junior Member
    Joined
    Dec 2007
    Posts
    25

    Dimensional Analysis

    So I understand how to solve dimensional analysis problems in general. What I don't understand is how to incorporate square/cubic yards into the answer. Here's two examples that I can't find the right answer for:

    1) LaShanda is buying carpet for a 15 feet x 12 feet room. How many square yards of carpet does she need to buy?

    2) Ted is planning a cement patio that measures 12 feet x 18 feet. If he wants the cement slab to be 4 inches thick, how many cubic yards of cement must he order?

    If anyone could break these down for me I'd really appreciate it.
    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    There are 9 square feet in a square yard and 27 cubic feet in a cubic yard.

    For #2, be sure to use consistent units. 4 inches = 1/3 feet
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2007
    Posts
    25
    galactus, thanks for the help but I'm still not quite getting it.

    The only ratios I'm given to use for these 2 problems are: "One yard is defined to be 3 feet. One foot is defined to be 12 inches." I'm pretty sure my professor wanted them done using those only, or using those to arrive other ratios (if necessary).

    For these questions I'm supposed to write them out in dimensional analysis form.
    Example:
    Convert the following measurement: 15 gallons to liters

    For this question I would answer:
    15 gallons * 4 quarts / 1 gallon. * 1 liter / 1.057 quarts = 56.76 liters

    For that one I was given "One liter is defined to be 1.057 quarts. There are 4 quarts in a gallon." I know I did that one correctly, it's just these that I can't grasp. If you could write them out in that format for me it would really help me out (it wouldn't be cheating, these are questions on a quiz I've already taken and am now studying for an exam with).

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    \frac{(15)(12)}{9} = 20 square yards.

    \frac{(12)(18)(1/3)}{27}=\frac{8}{3} cubic yards.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2006
    From
    Between my ears
    Posts
    62
    Thanks
    12
    Quote Originally Posted by Chizum View Post
    For this question I would answer:
    15 gallons * 4 quarts / 1 gallon. * 1 liter / 1.057 quarts = 56.76 liters
    In this example, you wrote out everything longhand and then dealt with the dimensions just like you would deal with numbers. For example, you have gallons in the numerator and denominator so you could eliminate them from the end result. You have quarts in the numerator and denominator so you could eliminate them from the result too. All you are left with is liters, which is what you want.

    For your other examples, just write them out longhand too, and then cross off all dimensions which appear in both numerator AND denominator:

    1) 15 feet * (1 yard/3 feet) * 12 feet * (1 yard/3 feet)

    The dimension feet is present on top and bottom of both halves of the equation so you can cross off each matching pair, leaving just yards:

    (15/3) yard * (12/3) yard = 20 square yards.

    2) 12 feet * (1 yard/3 feet) * 18 feet * (1 yard/3 feet) * 4 inches * (1 foot/12 inches) * (1 yard/3 feet)

    The dimension feet is present on top and bottom of the first two terms of this equation so you can cross off each matching pair. In the last term of this equation, there are units of feet AND inches on the top AND bottom so they can be crossed off too. Now you are left with yards:

    (12/3) yard * (18/3) yard * ((4/12)/3) yard = 8/3 cubic yards.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dimensional Analysis
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 7th 2011, 05:54 PM
  2. dimensional analysis help?
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: August 20th 2010, 08:37 PM
  3. Dimensional analysis check
    Posted in the Algebra Forum
    Replies: 0
    Last Post: January 7th 2010, 06:20 AM
  4. Dimensional Analysis check
    Posted in the Math Topics Forum
    Replies: 7
    Last Post: December 9th 2009, 12:36 AM
  5. Dimensional Analysis
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: August 2nd 2008, 06:59 AM

Search Tags


/mathhelpforum @mathhelpforum