A sheet of aluminum foil has a total area of 1.000 ft squared and a mass of 3.636 grams. What is the thickness of the foil in millimeters? (Density of Aluminum is 2.699 grams/cm cubed.)
volume of Al foil is area x thickness. You know the area. Volume can be calculated from mass = volume x density. You know density and mass. Post your work if you get stuck.
To find the thickness of the aluminum foil, you need to calculate its volume first.
1. Convert the area from square feet to square centimeters:
- 1 square foot = 929.03 square centimeters (approximately)
- So, the area of the aluminum foil is 929.03 cm²
2. Convert the mass from grams to kilograms:
- 1 gram = 0.001 kilograms
- So, the mass of the aluminum foil is 0.003636 kilograms
3. Calculate the volume of the aluminum foil using the density formula:
- Density = Mass / Volume
- Rearranging the formula, Volume = Mass / Density
- Volume = 0.003636 kg / 2.699 g/cm³
- Convert grams to kilograms, 1 g = 0.001 kg
- Volume = 0.003636 kg / 2.699 * 0.001 kg/cm³
- Volume = 0.003636 kg / 0.002699 kg/cm³
- Volume = 1.34667 cm³ (approximately)
4. Use the formula for the volume of a rectangular prism to find the thickness:
- Volume = Length * Width * Thickness
- Since the aluminum foil is very thin, we can assume that its thickness is equivalent to the height of the rectangular prism.
- The length and width are not given, but we know that the area is 929.03 cm².
- So, we can solve for one of the dimensions, assuming the other is 1 cm:
- Area = Length * Width
- 929.03 cm² = Length * 1 cm
- Length = 929.03 cm²
- Now, we can find the thickness:
- Volume = Length * Width * Thickness
- 1.34667 cm³ = 929.03 cm² * 1 cm * Thickness
- Thickness = 1.34667 cm³ / 929.03 cm²
- Thickness = 0.0014481 cm (approximately)
5. Convert the thickness from centimeters to millimeters:
- 1 centimeter = 10 millimeters
- So, the thickness of the aluminum foil is 0.014481 millimeters (approximately)
Therefore, the thickness of the aluminum foil is approximately 0.014481 millimeters.
To find the thickness of the aluminum foil, we need to use its mass, area, and the density of aluminum.
First, we need to convert the area from square feet to square centimeters, since the density is given in grams per cubic centimeter. Since 1 foot is equal to 30.48 centimeters, we can calculate the area in square centimeters as follows:
1 ft^2 = 30.48 cm * 30.48 cm = 929.0304 cm^2
Next, we need to convert the mass from grams to the same unit as the density. Since density is given in grams per cubic centimeter, we want the mass in grams. Therefore, no conversion is required in this case.
Now we can use the formula for density: Density = Mass / Volume.
Rearranging the formula to solve for volume, we get: Volume = Mass / Density.
The volume of the foil can be calculated as follows: Volume = 3.636 grams / 2.699 grams/cm^3 = 1.349 cm^3.
Finally, to find the thickness, we divide the volume by the area: Thickness = Volume / Area.
Substituting the values we calculated earlier, we have: Thickness = 1.349 cm^3 / 929.0304 cm^2.
Calculating this value yields: Thickness ≈ 0.001453 cm.
To convert this thickness to millimeters, we multiply by 10 (since there are 10 millimeters in 1 centimeter).
Therefore, the thickness of the aluminum foil is approximately 0.01453 millimeters.