How Thick Is the Paint on the Room's Walls?

AI Thread Summary
To determine the thickness of paint on the walls of a room measuring 12m by 12m by 8m, first calculate the total surface area of the four walls, which is 384 square meters. The total volume of paint used is converted from 3 gallons to approximately 0.01137 cubic meters. Using the formula for thickness (t = Volume/Area), the thickness of the paint layer is found to be 3.0 x 10^-5 meters. The calculations confirm that the problem is straightforward once the correct area and volume relationships are applied. Understanding these relationships is key to solving similar problems efficiently.
tensirk
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Homework Statement


You use exactly 3.0 gallons of paint to paint the walls of a room that measures 12 meters long by 12 meters wide by 8.0 meters high. How thick is the layer of paint that you put on the four walls? (No windows or doors) Use the conversion 1 gallon = 3.79 x 10-3m3.

Homework Equations


Possibly:
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
or
Volume of a Rectangular Prism = a b c
or Thickness= V/Area

The Attempt at a Solution


I converted the 3 gallons to m3 and got .01137 m3. I just am not really sure what to do next. I've tried playing around with the different formulas above, but nothing seems to come out right. The answer is supposed to be 3.0 x 10-5m. Seems like this question should be really easy...and it's making me feel really dumb for being unable to solve it. Any help would be much appreciated! Thanks!
 
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You should know that the area of the walls times the thickness of the paint folm is a volume, and you know what that volume is,

V = 3 * [1 gallon = 3.79 x 10-3m3] = A * t

A = 12*8 + 12*8 + 12*8 + 12*8

Solve for t

Good luck!
 
tensirk said:

Homework Statement


You use exactly 3.0 gallons of paint to paint the walls of a room that measures 12 meters long by 12 meters wide by 8.0 meters high. How thick is the layer of paint that you put on the four walls? (No windows or doors) Use the conversion 1 gallon = 3.79 x 10-3m3.

Homework Equations


Possibly:
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
or
Volume of a Rectangular Prism = a b c
or Thickness= V/Area

The Attempt at a Solution


I converted the 3 gallons to m3 and got .01137 m3. I just am not really sure what to do next. I've tried playing around with the different formulas above, but nothing seems to come out right. The answer is supposed to be 3.0 x 10-5m. Seems like this question should be really easy...and it's making me feel really dumb for being unable to solve it. Any help would be much appreciated! Thanks!

Don't forget you are not painting the roof or floor. What is the area of the walls? Area x Thickness = Volume of paint. It works out...
 

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