The density of a certain type of plastic is 0.89 g/cm3. If a sheet of this plastic is 10.0 m long, 1.0 m wide, and 1.0 cm thick, what is its mass?
To find the mass of the plastic sheet, we'll use the formula:
mass = density x volume
Given:
Density = 0.89 g/cm³
Length (l) = 10.0 m
Width (w) = 1.0 m
Thickness (t) = 1.0 cm
First, we need to convert the dimensions to the same unit. Since the density is given in grams per cubic centimeter (g/cm³), we'll convert the length and width from meters to centimeters.
1 meter = 100 centimeters
Length (l) = 10.0 m x 100 cm/m = 1000 cm
Width (w) = 1.0 m x 100 cm/m = 100 cm
Now we can calculate the volume (V) of the plastic sheet using the formula:
V = length x width x thickness
V = 1000 cm x 100 cm x 1.0 cm = 100,000 cm³
Now we can substitute the values into the formula for mass:
mass = density x volume
mass = 0.89 g/cm³ x 100,000 cm³ = 89,000 g
Therefore, the mass of the plastic sheet is 89,000 grams.
To find the mass of the plastic sheet, we need to use its density and dimensions. The formula for finding mass is:
Mass = Density × Volume
First, let's calculate the volume of the plastic sheet. The formula for volume is:
Volume = Length × Width × Height
In this case, the length (L) = 10.0 m, the width (W) = 1.0 m, and the height/thickness (H) = 1.0 cm = 0.01 m.
Substituting the values into the volume formula:
Volume = 10.0 m × 1.0 m × 0.01 m
= 0.1 m³
Now we have the volume, we can calculate the mass. Substituting the density (D) = 0.89 g/cm³ and the volume (V) = 0.1 m³ into the mass formula:
Mass = Density × Volume
= 0.89 g/cm³ × 0.1 m³
To ensure that the units cancel out correctly, we need to convert the density from grams per cubic centimeter (g/cm³) to grams per cubic meter (g/m³).
Since there are 1000 cm in 1 m, we can convert g/cm³ to g/m³ by multiplying the density by 1000:
Density (in g/m³) = Density (in g/cm³) × 1000
= 0.89 g/cm³ × 1000
= 890 g/m³
Now we can substitute the converted density value into the mass formula:
Mass = Density × Volume
= 890 g/m³ × 0.1 m³
= 89 g
Therefore, the mass of the plastic sheet is 89 grams.
dimensions=1Om x 1m x .01 m=1m^3
density=.89g/cm^3= .89E6/m^3
mass=.89E6=890kg