The relative density of an alloy is 6.5.a.find the mass of a solid cube of side 20cm.b.what volume of the alloy has a mass of 13kg
cc = cubic centimeter
density = 6.5 grams/cc
volume of cube = 20*20*20 = 8,000 cc
so
mass = 6.5 gms/cc *8, 000 cc = 52,000 gms = 52 Kg
13 kg (8,000cc/52kg) = 2,000 cc
a. To find the mass of a solid cube, you need to know the volume and the density of the material it is made from. In this case, the relative density of the alloy is given as 6.5.
Since relative density is the ratio of the density of the material to the density of water (which is 1 g/cm³), we can calculate the density of the alloy.
Density of the alloy = Relative density × Density of water
= 6.5 × 1 g/cm³
= 6.5 g/cm³
Now, let's calculate the mass of the solid cube:
Volume of the solid cube = (side length)^3
= (20 cm)^3
= 8000 cm³
Mass = Density × Volume
= 6.5 g/cm³ × 8000 cm³
= 52000 g
Therefore, the mass of the solid cube is 52000 grams (or 52 kilograms).
b. To find the volume of the alloy with a mass of 13 kg, we need to use the density of the alloy.
Mass = Density × Volume
Rearranging the equation, we can solve for volume:
Volume = Mass / Density
= 13,000 g / 6.5 g/cm³
Since the mass is given in kilograms, we need to convert it to grams by multiplying by 1000:
Volume = 13,000 g / 6.5 g/cm³
≈ 2000 cm³
Therefore, the volume of the alloy with a mass of 13 kg is approximately 2000 cm³.
To find the mass of a solid cube of side 20 cm, we can use the formula for the volume of a cube, which is V = s^3, where s represents the length of a side.
a. Find the mass of a solid cube of side 20 cm:
1. Calculate the volume of the cube:
V = 20 cm × 20 cm × 20 cm = 8,000 cm^3
2. To find the mass of the cube, we'll need to convert the volume from cubic centimeters to cubic meters because relative density is typically expressed in terms of the density of water at 4 degrees Celsius, which is 1 gram per cubic centimeter.
We divide the volume by 1,000,000 to convert cm^3 to m^3:
V = 8,000 cm^3 / 1,000,000 = 0.008 m^3
3. The relative density of the alloy is given as 6.5. Relative density is the ratio of the density of the substance to the density of water. Therefore, the density of the alloy = 6.5 × density of water.
The density of water is approximately 1000 kg/m^3.
Density of the alloy = 6.5 × 1000 kg/m^3 = 6500 kg/m^3
4. Calculate the mass of the solid cube:
Mass = Volume × Density = 0.008 m^3 × 6500 kg/m^3 = 52 kg
Therefore, the mass of a solid cube of side 20 cm is 52 kg.
b. To find the volume of the alloy that has a mass of 13 kg, we can use the formula to calculate volume:
1. Given mass = 13 kg
2. Given relative density = 6.5
Using the same calculation as above:
Density of the alloy = Relative density × Density of water = 6.5 × 1000 kg/m^3 = 6500 kg/m^3
3. We can rearrange the formula for mass and volume to solve for volume:
Volume = Mass / Density
Plugging in the values:
Volume = 13 kg / 6500 kg/m^3
4. Solve the equation:
Volume = 0.002 m^3
Therefore, the volume of the alloy with a mass of 13 kg is 0.002 m^3.