the relative density of an alloy is 6.5.find the mass of the solid alloy cube of side 20cm.what volume of the alloy has a mass of 13kg
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To find the mass of a solid alloy cube, we first need to know its volume. The volume of a cube is given by the formula:
Volume = Side^3
Given that the side of the cube is 20 cm, we can calculate the volume:
Volume = 20^3 = 8000 cm^3
Next, to find the mass of the cube, we can use the concept of relative density. The relative density of a substance is defined as the ratio of its density to the density of a reference substance, usually water. In this case, the relative density of the alloy is given as 6.5.
We know that the density (ρ) of a substance is calculated as:
Density = Mass / Volume
Rearranging the formula, we get:
Mass = Density x Volume
Since we are given the relative density, we need to find the actual density of the alloy. This can be done by multiplying the relative density by the density of water.
Density of water = 1000 kg/m^3 (approximately)
Density of alloy = Relative density x Density of water
= 6.5 x 1000 kg/m^3
= 6500 kg/m^3
Now we can calculate the mass of the cube:
Mass = Density x Volume
= 6500 kg/m^3 x (8000 cm^3 / 1000000)
= 52 kg
Therefore, the mass of the solid alloy cube of side 20 cm is 52 kg.
Now, to find the volume of the alloy that has a mass of 13 kg, we can rearrange the formula for density:
Density = Mass / Volume
Volume = Mass / Density
= 13 kg / 6500 kg/m^3
= 0.002 m^3
Therefore, the volume of the alloy with a mass of 13 kg is 0.002 m^3.