Question

1. zinc has a density of .719 g/cm³. if you have 20.0 lbs of zinc to galvanize sheet roofing to a depth of .5 mm, how many square meters of material can be galvanized? (454 g = 1 lb)

Explanation:

Step1: Convert mass of zinc to grams

We know that $454\ g = 1\ lb$. Given $m = 20.0\ lb$, then $m=20.0\times454\ g=9080\ g$.

Step2: Calculate volume of zinc

The density formula is $
ho=\frac{m}{V}$, where $
ho = 0.719\ g/cm^{3}$ and $m = 9080\ g$. Rearranging for $V$, we get $V=\frac{m}{
ho}=\frac{9080\ g}{0.719\ g/cm^{3}}\approx12628.65\ cm^{3}$.

Step3: Convert depth to centimeters

The depth $h = 0.5\ mm$. Since $1\ cm=10\ mm$, then $h = 0.05\ cm$.

Step4: Calculate area in square - centimeters

The volume formula for a thin - layer is $V = A\times h$, where $V$ is volume, $A$ is area and $h$ is height (or depth). Rearranging for $A$, we get $A=\frac{V}{h}=\frac{12628.65\ cm^{3}}{0.05\ cm}=252573\ cm^{2}$.

Step5: Convert area to square meters

Since $1\ m^{2}=10000\ cm^{2}$, then $A=\frac{252573\ cm^{2}}{10000}=25.2573\ m^{2}\approx25.3\ m^{2}$.

Answer:

$25.3\ m^{2}$