A full can of soda has a mass of 0.421 kg. It contains 3.57 x 10-4 m3 of liquid. Assuming that the soda has the same density as water, find the volume of aluminum used to make the can.
Volume of liquid
=3.57*10^-4 m^3
=357 ml
mass of liquid
=357 g
mass of aluminium (can)
=421-357
=64 g
density of aluminium = 2.7 g/ml
Volume of aluminium = 64/2.7 cc
= 23.7 cc
To find the volume of aluminum used to make the can, we need to subtract the volume of the liquid (soda) from the total volume of the can.
First, we can find the volume of the liquid by multiplying the height of the soda in the can by the area of the base. We can assume that the can is cylindrical, so the formula for the volume of a cylinder is:
Volume of liquid = height * area of the base
Given:
Mass of the soda = 0.421 kg
Density of water (assumed density of the soda) = 1000 kg/m³
Volume of liquid = 3.57 x 10^-4 m³
Next, we need to find the height of the soda in the can:
Density = Mass / Volume
Density of water (soda) = Mass of the soda / Volume of the liquid
Rearranging the formula to solve for the height:
Mass of the soda = Density of water (soda) * Volume of the liquid
Height = Mass of the soda / (Density of water (soda) * Area of the base)
Now we can calculate the volume of aluminum used to make the can:
Volume of the can = Total volume - Volume of liquid
We are given that the total volume of the can is the same as the volume of the liquid.
Therefore, the volume of aluminum used to make the can is 0 m³ (or 0 liters), assuming there is no space between the liquid and the can.
To find the volume of aluminum used to make the can, we need to subtract the volume of the liquid from the total volume of the can.
Given:
Mass of soda can = 0.421 kg
Volume of liquid = 3.57 x 10^(-4) m^3
We can assume that the soda can is completely filled with liquid, so the total volume of the can is equal to the volume of the liquid.
Since the soda has the same density as water, we can use the formula:
Density = Mass / Volume
Rearranging the formula, we can solve for the volume:
Volume = Mass / Density
The density of water is approximately 1000 kg/m^3.
Substituting the values into the formula:
Volume = 0.421 kg / 1000 kg/m^3
Volume = 4.21 x 10^(-4) m^3
Now, subtracting the volume of the liquid from the total volume of the can:
Volume of aluminum = Total volume of the can - Volume of liquid
Volume of aluminum = 4.21 x 10^(-4) m^3 - 3.57 x 10^(-4) m^3
Volume of aluminum = (4.21 - 3.57) x 10^(-4) m^3
Volume of aluminum = 0.64 x 10^(-4) m^3
Therefore, the volume of aluminum used to make the can is 0.64 x 10^(-4) m^3.