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The question is: "One gallon of paint covers an area of $25.0 \space m^2$. What is the thickness of the paint on the wall? Express your answer in micrometers."

I don't think it's possible to convert area to distance, so I'm assuming that I'm supposed to convert that number into $μm^2$ instead.

I did $$25.0 \space m * 1\space m *(\frac{1,000,000 \space um^2}{1\space m})^2 = 2.50e13$$

This wasn't correct however, and I'm completely clueless about what other options I have at solving this.

Anton Vrdoljak
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Beerus Doggo
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    Hint: (Area) $ \times $ (thickness) = Volume of the paint. Furthermore 1 gallon =0.00378541 cubic meter. – Anurag A Aug 23 '20 at 05:34
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    You’re not asked to give an area in micrometres: you’re asked for the thickness in micrometres, and thickness is measured in linear units. What you need to work out is the volume (in suitable metric units) of a gallon of paint. – Brian M. Scott Aug 23 '20 at 05:35

1 Answers1

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Hint: $\space V = A \cdot h \iff h = \frac{V}{A}$

$V$ is volume, and in our case we have $V = 1$ gallon $=3.785$ liters $= 3.785 \space dm^3$;

$A$ is area, and in our case we have $A = 25\space m^2 = 2\space 500 \space dm^2$;

$h$ is thickness, and in our case it is unknown!

$$h=\frac{3.785 \space dm^3}{2 \space 500 \space dm^2}=1.514\cdot 10^{-3} \space dm = \boxed{1 \space514 \space \mu m}.$$

Anton Vrdoljak
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