# Dimensional Analysis

• Dec 6th 2007, 03:12 PM
Chizum
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.
• Dec 6th 2007, 04:05 PM
galactus
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
• Dec 6th 2007, 05:57 PM
Chizum
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).

• Dec 6th 2007, 06:08 PM
galactus
$\displaystyle \frac{(15)(12)}{9}$ = 20 square yards.

$\displaystyle \frac{(12)(18)(1/3)}{27}=\frac{8}{3}$ cubic yards.
• Dec 6th 2007, 06:53 PM
DavidB
Quote:

Originally Posted by Chizum
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.