The relative density of an alloy is 6.5,
a) find the mass of a solid alloy cube of side 20cm, what volume of the alloy has a mass of 15kg
To find the mass of a solid alloy cube of side 20 cm, we need to use the formula for the volume of a cube, which is given by:
Volume = side^3
In this case, the side length of the cube is 20 cm, so the volume would be:
Volume = 20 cm * 20 cm * 20 cm = 8000 cm^3
Now, let's move on to finding the mass of the alloy. We are given the relative density of the alloy as 6.5. The relative density is defined as the ratio of the density of the alloy to the density of water. In mathematical terms:
Relative Density = Density of Alloy / Density of Water
Density of Alloy = Relative Density * Density of Water
Since the density of water is 1000 kg/m^3 (or equivalently, 1 g/cm^3), the density of the alloy would be:
Density of Alloy = 6.5 * 1000 kg/m^3 = 6500 kg/m^3
Now, we can calculate the mass of the alloy using the formula:
Mass = Density * Volume
Mass = 6500 kg/m^3 * 8000 cm^3
First, we need to convert the volume from cm^3 to m^3. To do this, divide the volume by 1,000,000:
Volume = 8000 cm^3 / 1000000 = 0.008 m^3
Now, we can calculate the mass:
Mass = 6500 kg/m^3 * 0.008 m^3 = 52 kg
Therefore, the mass of the solid alloy cube with a side length of 20 cm is 52 kg.
Next, let's find the volume of the alloy that has a mass of 15 kg. We can rearrange the formula for mass to solve for volume:
Volume = Mass / Density
Since we know the mass is 15 kg and the density is 6500 kg/m^3:
Volume = 15 kg / 6500 kg/m^3 = 0.0023 m^3
Now, we need to convert the volume from m^3 to cm^3 by multiplying by 1,000,000:
Volume = 0.0023 m^3 * 1000000 = 2300 cm^3
Therefore, the volume of the alloy that has a mass of 15 kg is 2300 cm^3.