If aluminum has a density of 2.7g/cm^3,what is the mass,in grams of the foil?
It states that a package of aluminum foil is 54.3 yd long, 14 inches wide, and 0.00035 inches thick.
To find the mass of the aluminum foil, we need to calculate its volume first using the given dimensions and density. Here are the steps:
Step 1: Convert the length and width to the same unit.
The given length is 54.3 yards, and 1 yard is equal to 3 feet.
So, the length in feet = 54.3 x 3 = 162.9 feet.
The given width is 14 inches. And 1 foot is equal to 12 inches.
So, the width in feet = 14 / 12 = 1.167 feet.
Step 2: Convert the thickness to feet.
The given thickness is 0.00035 inches. And 1 foot is equal to 12 inches.
So, the thickness in feet = 0.00035 / 12 = 0.0000291667 feet.
Step 3: Calculate the volume of the aluminum foil.
Volume = length x width x thickness
Volume = 162.9 feet x 1.167 feet x 0.0000291667 feet
Step 4: Convert the volume to cm^3.
Since 1 foot is equal to 30.48 cm, we can convert the volume in feet to volume in cm as follows:
Volume in cm^3 = Volume in feet^3 x (30.48 cm / 1 foot)^3
Step 5: Calculate the mass using the density.
Mass = Volume x Density
Now, let's calculate the mass of the aluminum foil step-by-step.
Step 1:
Length in feet = 54.3 x 3 = 162.9 feet
Width in feet = 14 / 12 = 1.167 feet
Step 2:
Thickness in feet = 0.00035 / 12 = 0.0000291667 feet
Step 3:
Volume = 162.9 feet x 1.167 feet x 0.0000291667 feet
Step 4:
Volume in cm^3 = Volume in feet^3 x (30.48 cm / 1 foot)^3
Step 5:
Mass = Volume in cm^3 x Density
Now, let's calculate the values:
Step 1:
Length in feet = 162.9 feet
Width in feet = 1.167 feet
Step 2:
Thickness in feet = 0.0000291667 feet
Step 3:
Volume = 162.9 feet x 1.167 feet x 0.0000291667 feet
Step 4:
Volume in cm^3 = Volume in feet^3 x (30.48 cm / 1 foot)^3
Volume in cm^3 = 162.9 x 1.167 x 0.0000291667 x (30.48)^3 cm^3
Step 5:
Mass = Volume in cm^3 x Density
Mass = (162.9 x 1.167 x 0.0000291667 x (30.48)^3) cm^3 x 2.7 g/cm^3
After performing the calculations, the mass of the aluminum foil is obtained in grams.
To find the mass of the aluminum foil, we need to calculate the volume of the foil first.
First, let's convert the dimensions of the foil from yards and inches into centimeters to be consistent with the density unit (g/cm^3).
1 yard = 91.44 cm (approximately)
1 inch = 2.54 cm
Length of the foil in cm = 54.3 yd * 91.44 cm/yd = 4970.392 cm
Width of the foil in cm = 14 inches * 2.54 cm/inch = 35.56 cm
Thickness of the foil in cm = 0.00035 inches * 2.54 cm/inch = 0.000889 cm
Next, we can calculate the volume using the formula:
Volume = Length * Width * Thickness
Volume of the foil = 4970.392 cm * 35.56 cm * 0.000889 cm = 156.01 cm^3
Now, we can find the mass of the foil by multiplying the volume by the density:
Mass = Volume * Density
Mass of the foil = 156.01 cm^3 * 2.7 g/cm^3 = 421.227 g
Therefore, the mass of the aluminum foil is approximately 421.227 grams.