The mean radius of the Earth is 6.37 x 106 meters (m). Assuming the earth can be modeled as a perfect sphere
a. In cubic meters (m3 ) what is the volume of the Earth?
b. In meters (m) what is Earth’s circumference?
c. If the mean density is 5.515g/cm3, what is the Earth’s mass in kilograms (kg)?
To solve these questions, we'll need to use some basic formulas related to the geometry of a sphere.
a. Volume of the Earth:
The formula to find the volume of a sphere is given by V = (4/3)πr^3, where V is the volume and r is the radius.
Using the given mean radius of the Earth (6.37 x 10^6 meters), we can substitute this value into the formula and calculate the volume.
V = (4/3) x π x (6.37 x 10^6)^3
= (4/3) x 3.14 x (6.37 x 10^6)^3
≈ 1.08321 x 10^21 cubic meters
Therefore, the volume of the Earth is approximately 1.08321 x 10^21 cubic meters.
b. Circumference of the Earth:
The formula to find the circumference of a sphere is given by C = 2πr, where C is the circumference and r is the radius.
Using the given mean radius of the Earth (6.37 x 10^6 meters), we can substitute this value into the formula and calculate the circumference.
C = 2π x (6.37 x 10^6)
= 2 x 3.14 x (6.37 x 10^6)
≈ 4.00278 x 10^7 meters
Therefore, the Earth's circumference is approximately 4.00278 x 10^7 meters.
c. Earth's mass:
To find the Earth's mass, we need to use the formula: Mass = Density x Volume.
Using the given mean density of the Earth (5.515 g/cm^3) and the volume we calculated earlier, we can calculate the mass in kilograms.
First, we need to convert the density from grams per cubic centimeter (g/cm^3) to kilograms per cubic meter (kg/m^3).
Density in kg/m^3 = Density in g/cm^3 x 1000
Density in kg/m^3 = 5.515 g/cm^3 x 1000
= 5515 kg/m^3
Now we can substitute the density and volume into the formula:
Mass = Density x Volume
= 5515 kg/m^3 x 1.08321 x 10^21 m^3
= 5.97 x 10^24 kg
Therefore, the Earth's mass is approximately 5.97 x 10^24 kilograms.