The Average density of Earth is 5.52g/cm^3. What is its density in a. kg/m^3 b. lb/ft^3. Please help me set up these equations. Thank you!
5.52 g/cc.
You want to multiply the 5.52 g/cc by factors so that g is changed to kg and cc (cubic cm) is changed to m^3. I'm sure you have heard of dimensional analysis.
We can change one unit at a time.
1000 g = 1 kg
5.52 g x (1 kg/1000g) = 0.00552 kg/cc.
There are 100 cm to 1 m
0.00552 kg/cubic cm x (100 cm/m)(100 cm/m)(100 cm/m) = 5520 kg/m^3.
That's how you do it. I'll let you do the one on lbs/ft^3.
By the way, you can always check your answer by typing the problem into google. For example, for the above type into the google window the following without the quotation marks.
"5.52 g/cc to kg/m^3" and hit the enter button. 5520 kg/m^3 will be returned as the answer.
Ah, density calculations, Earth's favorite topic! Here we go with some laughs to help you set up those equations, my friend:
a. To find the density in kg/m^3, we need to convert grams to kilograms and cubic centimeters to cubic meters.
So, density (kg/m^3) = 5.52g/cm^3 * (1kg / 1000g) * (1m^3 / 1e6 cm^3).
Now, let's do some math without causing a gravitational pull:
Density (kg/m^3) = 5.52 * 1 / 1000 * 1 / 1e6 = 5.52e-6 kg/m^3
There you have it, Earth's density in a more metric-friendly unit!
b. Now, let's convert Earth's density to lb/ft^3, spicing things up with some imperial humor!
Density (lb/ft^3) can be calculated as follows:
Density (lb/ft^3) = 5.52g/cm^3 * (1lb / 453.6g) * (1ft^3 / (30.48cm)^3)
And get ready for the punchline:
Density (lb/ft^3) = 5.52 * 1 / 453.6 * 1 / (30.48)^3 ≈ 0.322 lb/ft^3
There you go, my friend! Earth's density in both metric and imperial units. Hope I could bring a smile to your face with these equations!
To convert the average density of Earth from grams per cubic centimeter (g/cm^3) to other units, we can use the following conversion factors:
1 g/cm^3 = 1000 kg/m^3 (for part a)
1 g/cm^3 = 62.43 lb/ft^3 (for part b)
a. To convert the density to kg/m^3:
Let's set up the equation:
Density (kg/m^3) = Density (g/cm^3) * Conversion factor
Substituting the given values:
Density (kg/m^3) = 5.52 g/cm^3 * 1000 kg/m^3
Therefore, the density of Earth in kg/m^3 is 5520 kg/m^3.
b. To convert the density to lb/ft^3:
Let's set up the equation:
Density (lb/ft^3) = Density (g/cm^3) * Conversion factor
Substituting the given values:
Density (lb/ft^3) = 5.52 g/cm^3 * 62.43 lb/ft^3
Therefore, the density of Earth in lb/ft^3 is 344.3196 lb/ft^3 (rounded to four decimal places).
To convert the density of Earth from grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3), you need to use the following conversion factors:
1 g/cm^3 = 1000 kg/m^3
To set up the equation, you can use the following formula:
Density in kg/m^3 = Density in g/cm^3 * Conversion factor
a. To convert to kg/m^3, the equation becomes:
Density in kg/m^3 = 5.52 g/cm^3 * 1000 kg/m^3
b. To convert to lb/ft^3, you will need to use an additional conversion factor:
1 kg/m^3 = 0.0624 lb/ft^3
So, the equation to convert to lb/ft^3 becomes:
Density in lb/ft^3 = 5.52 g/cm^3 * 1000 kg/m^3 * 0.0624 lb/ft^3
Now you can evaluate these equations to find the density of Earth in the desired units.
a. Density of Earth in kg/m^3 = 5.52 * 1000 = 5520 kg/m^3.
b. Density of Earth in lb/ft^3 = 5.52 * 1000 * 0.0624 = 345.6 lb/ft^3.
So, the density of Earth is 5520 kg/m^3 in SI units and 345.6 lb/ft^3 in imperial units.