Finding Surface Area in square feet with Volume & Thickness

In summary, Homework Equations say that the surface area of a 1 gallon paint can cover 0.1337 ft2 with a 0.1 cm thick coat.
  • #1
Oannes
26
1

Homework Statement


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?

Homework 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

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.
 
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  • #2
Oannes said:
divide cubed feet by ft resulting in square feet
Perfectly legal.
 
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  • #3
@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.
 
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  • #4
LCKurtz said:
@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.

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
@Bystander thanks a bunch I was sweating it! lol
 

1. How do you calculate the surface area in square feet with volume and thickness?

To calculate the surface area in square feet, you will need to first determine the volume and thickness of the object. Then, you can use the formula SA = V/T to find the surface area in square feet.

2. Can you provide an example of finding surface area in square feet with volume and thickness?

Sure! Let's say we have a rectangular prism with a volume of 100 cubic feet and a thickness of 5 feet. Using the formula SA = V/T, we can calculate the surface area as 100/5 = 20 square feet.

3. What units are typically used for volume, thickness, and surface area in this calculation?

The most common units used for volume, thickness, and surface area in this calculation are cubic feet, feet, and square feet, respectively. However, you can use any units as long as they are consistent throughout the calculation.

4. Are there any other formulas for finding surface area in square feet with volume and thickness?

Yes, there are other formulas that can be used depending on the shape of the object. For example, the formula for finding the surface area of a cube is SA = 6s^2, where s is the length of one side. It's important to use the correct formula for the specific shape of the object.

5. Why is it important to know the surface area in square feet with volume and thickness?

Knowing the surface area in square feet is important for many practical applications, such as determining the amount of paint or material needed to cover an object, calculating heat transfer in engineering, or determining the cost of packaging for a product. It is also a fundamental concept in geometry and can help us understand the properties of different shapes.

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