The relative Density of an alloy is 65.(a) find the mass of a solid alloy cube of side 20cm.(b) what vol of the alloy has a mass of 13kg? Please explain in details
Density is not a dimensionless quantity. You have to tell us what the units are. Just saying "65" is not enough. It cannot be 65 g/cm^3. There are no alloys that dense.
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To answer these questions, we need to understand the concept of relative density and apply the appropriate formulas. Relative density, also known as specific gravity, is the ratio of the density of a substance to the density of another substance, usually a reference material.
(a) To find the mass of a solid alloy cube with a side length of 20 cm, we need to know the density of the alloy. Unfortunately, the given information only mentions the relative density. Therefore, we'll need to assume a reference material with a known density to calculate the actual density of the alloy.
Let's assume the density of water as the reference material, which is 1000 kg/m³. The relative density (RD) is the ratio of the density of the alloy (ρ_alloy) to the density of water (ρ_water):
RD = ρ_alloy / ρ_water
Given that the relative density of the alloy is 65, we can set up the equation as follows:
65 = ρ_alloy / 1000
To find the density of the alloy, we can rearrange the equation:
ρ_alloy = 65 * 1000
ρ_alloy = 65000 kg/m³
Now, we can calculate the mass (m) of the alloy cube using the formula:
m = ρ_alloy * V
where V is the volume. The volume of a cube is given by:
V = side³
Therefore, the volume of the alloy cube is:
V = (0.2 m)³ = 0.008 m³
Now, we can substitute the values to find the mass:
m = 65000 kg/m³ * 0.008 m³ = 520 kg
Hence, the mass of the solid alloy cube with a side length of 20 cm is 520 kg.
(b) To find the volume of the alloy that has a mass of 13 kg, we can rearrange the mass formula to solve for volume:
m = ρ_alloy * V
V = m / ρ_alloy
Substituting the given mass (m = 13 kg) and the density of the alloy (ρ_alloy = 65000 kg/m³) into the equation:
V = 13 kg / 65000 kg/m³ = 0.0002 m³
Therefore, the volume of the alloy that has a mass of 13 kg is 0.0002 m³.