To solve this problem, we use the formula:
density = mass / volume
a. Density of aluminium = 3 kg/m³
We are given that the mass of the cube of aluminium is 24 kg. So, we can calculate its volume using the formula:
volume = mass / density
volume = 24 / 3
volume = 8 m³
Since the cube has a side length of 2 meters, its volume is given by:
volume = side³
8 = 2³
Therefore, the density of the cube is the same as the density of aluminium, which is 3 kg/m³.
b. Density of aluminium = 12 kg/m³
We are given that the mass of the cube of aluminium is 24 kg, and its side length is 2 meters. So, we can calculate its volume as:
volume = side³
volume = 2³
volume = 8 m³
Now we can use the formula to calculate the density:
density = mass / volume
density = 24 / 8
density = 3 kg/m³
The density of the cube is the same as the density of aluminium, which is 3 kg/m³.
c. Density of aluminium = 24 kg/m³
Using the same approach as before, we can calculate the volume of the cube:
volume = mass / density
volume = 24 / 24
volume = 1 m³
Since the side length of the cube is not given, we cannot calculate it directly. However, if we assume that the cube is a regular cube, then its volume is given by:
volume = side³
Therefore, we can calculate the side length as:
side = cube root of (volume)
side = cube root of (1)
side = 1 meter
So, if the cube is a regular cube with a side length of 1 meter, then its density is 24 kg/m³.
d. Density of aluminium = 48 kg/m³
Using the same approach as earlier:
volume = side³
volume = 24 / 48
volume = 0.5 m³
If we assume that the cube is a regular cube, then its volume is given by:
volume = side³
Therefore, we can calculate the side length as:
side = cube root of (0.5)
side = 0.79 meters
So, if the cube is a regular cube with a side length of 0.79 meters, then its density is 48 kg/m³.