A package of aluminum foil covers 75.0 ft^2 and weighs 12 oz. Aluminum has a density of 2.70 g/mL. What is the thickness of the foil in millimeters?
(1 in = 2.54 cm, 1 oz = 28.4 g, 1 mL = 1 cm^3)
Convert 75.0 ft^2 to cm^2. Convert 12 oz to grams. Use mass = volume x density to solve for volume, then
volume = area x thickness.
Solve for thickness and convert to mm.
ilijl
To find the thickness of the aluminum foil, we need to calculate the volume of the foil first.
We know that the density of aluminum is 2.70 g/mL. Given that 1 mL = 1 cm^3, we can convert the density to 2.70 g/cm^3.
The mass of the foil is given as 12 oz, which we can convert to grams by multiplying by the conversion factor 28.4 g/oz. Therefore, the mass of the foil is 340.8 g (12 oz * 28.4 g/oz).
Next, we need to find the volume of the foil in cm^3. To do this, we divide the mass by the density:
Volume = Mass / Density
Volume = 340.8 g / 2.70 g/cm^3
Volume = 126.22 cm^3
Now, we can find the thickness of the foil by dividing the volume by the area.
Area = 75.0 ft^2
Since 1 ft = 12 in and 1 in = 2.54 cm, we can convert the area to cm^2:
Area = 75.0 ft^2 * (12 in/ft)^2 * (2.54 cm/in)^2
Area = 6532.16 cm^2
Finally, to find the thickness, we divide the volume in cm^3 by the area in cm^2:
Thickness = Volume / Area
Thickness = 126.22 cm^3 / 6532.16 cm^2
Thickness ≈ 0.019 cm
Since the question asks for the thickness in millimeters, we can convert the result to millimeters by multiplying by 10.
Thickness ≈ 0.019 cm * 10
Thickness ≈ 0.19 mm
Therefore, the thickness of the aluminum foil is approximately 0.19 mm.