The diameter of some celestial body is 3080 km. What is the volume of this body?
_____m3
How many of these celestial bodies would be needed to create a volume equal to that of Earth? The radius of the Earth is 6.38 106 m.
To find the volume of a celestial body with a given diameter, we can use the formula for the volume of a sphere:
Volume = (4/3) * π * (radius)^3
First, let's find the radius of the celestial body using the given diameter of 3080 km. The formula to convert diameter to radius is:
Radius = Diameter / 2
Therefore, the radius of the celestial body is 3080 km / 2 = 1540 km.
Next, we need to convert the radius from kilometers to meters since the unit for volume is cubic meters. To convert kilometers to meters, we multiply by 1000:
Radius = 1540 km * 1000 = 1,540,000 m
Now we can substitute the radius value into the volume formula:
Volume = (4/3) * π * (1,540,000)^3 m^3
Using a calculator to compute this, we find that the volume of the celestial body is approximately 6.661 x 10^18 m^3.
To determine how many of these celestial bodies would be needed to create a volume equal to that of Earth, we need to compare their volumes. The radius of the Earth is given as 6.38 x 10^6 m.
Using the volume formula again, we can find the volume of Earth:
Volume of Earth = (4/3) * π * (6.38 x 10^6)^3 m^3
Using a calculator to compute this, we find that the volume of Earth is approximately 1.083 x 10^21 m^3.
Now, we can divide the volume of Earth by the volume of the celestial body to determine how many of these celestial bodies would be needed:
Number of celestial bodies = Volume of Earth / Volume of a celestial body
Number of celestial bodies = (1.083 x 10^21 m^3) / (6.661 x 10^18 m^3)
Using a calculator to compute this, we find that approximately 162 celestial bodies would be needed to create a volume equal to that of Earth.