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 calculate the volume of a celestial body, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
where V is the volume and r is the radius.
The diameter of the celestial body given is 3080 km. To find the radius, we divide the diameter by 2:
r = 3080 km / 2 = 1540 km
To convert this to meters, we multiply by 1000:
r = 1540 km * 1000 = 1,540,000 m
Now we can use this radius value to calculate the volume of the celestial body:
V = (4/3) * π * (1,540,000 m)^3
Calculating this will give us the volume of the celestial body in cubic meters.
Now, let's calculate the volume using the formula:
V = (4/3) * 3.14159 * (1,540,000 m)^3
V ≈ 1.01 * 10^18 m^3
Therefore, the volume of the celestial body is approximately 1.01 x 10^18 cubic meters.
To find out how many of these celestial bodies would be needed to create a volume equal to that of Earth, we need to calculate the volume of Earth and divide it by the volume of the celestial body.
The radius of Earth is given as 6.38 * 10^6 m. We can use the same formula as before to calculate its volume:
V_earth = (4/3) * π * (6.38 * 10^6 m)^3
Calculating this will give us the volume of Earth in cubic meters.
Now, let's calculate the volume of Earth:
V_earth = (4/3) * 3.14159 * (6.38 * 10^6 m)^3
V_earth ≈ 1.09 * 10^21 m^3
Now we can divide the volume of Earth by the volume of the celestial body to find out how many celestial bodies would be needed to create a volume equal to that of Earth:
Number of celestial bodies = V_earth / V_celestial
Number of celestial bodies ≈ (1.09 * 10^21 m^3) / (1.01 * 10^18 m^3)
Number of celestial bodies ≈ 1079.2
Therefore, approximately 1079 celestial bodies with a volume equal to the given celestial body would be needed to create a volume equal to that of Earth.