a piece of metal has a mass of 85 cg and a volume of 450L. What is its density in g/cm^3? What would be the mass of 300cm^3 of this metal? What would be the volume of 200 ounces of this metal?
Ah, metal, the Arnold Schwarzenegger of materials! Let's do some math and flex those brain muscles.
To find the density of the metal, we can use the formula: density = mass / volume.
Given that the mass is 85cg and volume is 450L, we need to convert them to matching units. One centigram (cg) is equal to 0.01 grams (g), and one liter (L) is equal to 1000 cubic centimeters (cm^3). Now, let's crunch those numbers!
First, let's convert the mass: 85cg = 85 * 0.01g = 0.85g.
Now, let's convert the volume: 450L = 450 * 1000cm^3 = 450,000cm^3.
Next, calculate the density: density = mass / volume = 0.85g / 450,000cm^3.
That gives us the density in g/cm^3.
For the mass of 300cm^3 of this metal, we can use the density we just calculated and the formula: mass = density * volume.
Substituting the values, we get: mass = (0.85g/cm^3) * 300cm^3.
Lastly, let's tackle the volume of 200 ounces of this metal. But hold on, ounces are not commonly used for measuring volume. Ounces are typically used for weight!
So, to find the volume, we would need the density of the metal in ounces per cubic inch (oz/in^3). Once we have that, we can use the formula: volume = mass / density.
But since we don't have the density in ounces, let's stick to the previous calculations and leave it at that.
Remember, laughter can be the best formula for learning!
To find the density of the metal in g/cm^3, divide the mass (in grams) by the volume (in cm^3).
Given:
Mass of the metal = 85 cg
Volume of the metal = 450 L
1. To convert the mass from centigrams (cg) to grams (g), divide by 100 since 1 cg = 0.01 g:
Mass of the metal = 85 cg / 100 = 0.85 g
2. To convert the volume from liters (L) to cm^3, multiply by 1000 since 1 L = 1000 cm^3:
Volume of the metal = 450 L * 1000 = 450000 cm^3
Now we can calculate the density:
Density = Mass / Volume
Density = 0.85 g / 450000 cm^3
Density ≈ 0.0000018889 g/cm^3 (rounded to 5 decimal places)
Next, let's calculate the mass of 300 cm^3 of this metal:
Mass = Density * Volume
Mass = 0.0000018889 g/cm^3 * 300 cm^3
Mass ≈ 0.00056667 g (rounded to 5 decimal places)
Finally, let's calculate the volume of 200 ounces of this metal:
To convert ounces (oz) to grams (g), multiply by 28.3495 since 1 oz = 28.3495 g:
Mass in grams = 200 oz * 28.3495 g/oz
Mass in grams ≈ 5669.9 g (rounded to 1 decimal place)
Since we already know the density of the metal, we can use it to find the volume:
Volume = Mass / Density
Volume = 5669.9 g / 0.0000018889 g/cm^3
Volume ≈ 2999999.46 cm^3 (rounded to 2 decimal places)
To find the density of the metal, you need to divide its mass by its volume. Density is typically expressed in units of grams per cubic centimeter (g/cm^3).
1. Density in g/cm^3:
Given that the mass of the metal is 85 centigrams (cg) and the volume is 450 liters (L), we need to convert the units to grams (g) and cubic centimeters (cm^3) respectively, before calculating the density.
Converting the mass from centigrams to grams:
1 gram (g) = 100 centigrams (cg)
So, 85 cg = 85/100 g = 0.85 g
Converting the volume from liters to cubic centimeters:
1 liter (L) = 1000 cubic centimeters (cm^3)
So, 450 L = 450 * 1000 cm^3 = 450000 cm^3
Now we can calculate the density:
Density = mass/volume
Density = 0.85 g / 450000 cm^3 = 0.00000188889 g/cm^3 (rounded to 5 decimal places)
Therefore, the density of the metal is approximately 0.00000188889 g/cm^3.
2. Mass of 300cm^3 of this metal:
To find the mass of 300 cubic centimeters (cm^3) of this metal, you can use the density you calculated earlier.
Mass = Density * Volume
Mass = 0.00000188889 g/cm^3 * 300 cm^3 = 0.00056667 g
Therefore, the mass of 300 cm^3 of this metal would be approximately 0.00056667 g.
3. Volume of 200 ounces of this metal:
First, we need to convert ounces (oz) to grams (g) because the density is given in grams per cubic centimeter (g/cm^3).
1 ounce (oz) ≈ 28.35 grams (g)
So, 200 ounces = 200 * 28.35 g = 5670 g
Now, we can use the density to calculate the volume:
Volume = Mass / Density
Volume = 5670 g / 0.00000188889 g/cm^3 = 3,001,125,000 cm^3
Therefore, the volume of 200 ounces of this metal would be approximately 3,001,125,000 cm^3.