# Homework Help: Finding Surface Area in square feet with Volume & Thickness

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1. Sep 8, 2016

### Oannes

1. The problem statement, all variables and given/known data
How large a surface area in units of square feet will 1 gallon of paint cover if we apply a coat of paint that is 0.1cm thick?

2. Relevant equations
Since Volume is L * W * H and we can assume the object is square besides the height which in this case will be the thickness. So since Volume = area * thickness then we can say that the area is Volume/Thickness. So:

Surface Area = Volume / Thickness
x ft2 = 1gallon / 0.1 cm

3. The attempt at a solution
First I converted gallons to cubic feet which would give me the volume. There is .264 gallons in a liter, and .0353 cubic feet in a Liter. Therefore:

(1gal)(1L/.264gal)(.0353ft3/1L) = 0.1337ft3

Second I converted .1cm to feet, this was much easier:

(.1cm)(1m/100cm)(3.28ft/1m) = .00328ft

Thirdly I plugged them into the equation for finding Surface Area:

SA = (.1337ft3/.00328ft)

Resulting in:

SA = 40.76ft2

My Question: I feel that I worked this problem correctly but I am not sure and want to be positive that all the steps I followed are correct. My biggest issue is wondering if I can divide cubed feet by ft resulting in square feet. I believe this to be possible for you can do this with variables with exponents power of 3 in the numerator and to the power of 1 in the denominator, but I just want to be sure. If something is wrong I would appreciate any help in guiding me in the right direction. Thanks in advance for any help given, this problem racked my brain for a while until I started to think about what volume truly was in respect to dimensions.

2. Sep 8, 2016

### Bystander

Perfectly legal.

3. Sep 9, 2016

### LCKurtz

@Oannes: What you did is fine. Here's a suggestion on how you might organize it that you might like. You started with$$x~ \text{ft}^2 = \frac {1 \text{gal}}{0.1 \text{cm}}$$Now you can just multiply by one conversion fraction after another like this:$$x~ \text{ft}^2 = \frac {1 \text{gallon}}{0.1 \text{cm}} \cdot \frac{.133681\text{ft}^3}{1~\text{gallon}} \cdot\frac{12\text{in}}{1~\text{ft}}\cdot \frac{2.54\text{cm}}{1~\text{inch}}=40.745\text{ft}^2$$Each conversion fraction changes the units, cancelling the old and putting in the new units. I did a slightly different string of conversions, but that's the nice thing about the method. Do it in any order you like, changing the units along the way.

4. Sep 9, 2016

### Oannes

Thanks for the help with cleaning up my problem, I tend to be messy and as a result of that I sometimes lose where I am! Thanks so much!

5. Sep 9, 2016

### Oannes

@Bystander thanks a bunch I was sweating it! lol