The diameter of the Moon is 3480km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to the Earth?
How do you find the volume of the Moon from just the diameter? Also, does anybody know how to figure out the volume of the Earth?
The earth's diameter is 3.67 times that of the moon. Since volume is proportional to diameter cubed, the earth's volume is (3.67)^3 = 49 times larger.
http://www.wikihow.com/Calculate-the-Volume-of-a-Sphere
The diameter of the eath according to Google is 12,756.2 km.
We assume both the earth and the moon have a shape close enough to a sphere, therefore we use the formula formula for the volume of a sphere as suggested by Ms Sue.
Volume of the moon
= (4/3)πr³
= (4/3)π(3480/2)³
= 2.206*1010 km³
The volume of the earth can be calculated similarly using diameter = 12,756.2 km (reference Google).
To find the volume of a sphere, including the Moon, you'll need to use the formula:
Volume = (4/3) * π * (radius^3)
But since you only have the diameter of the Moon, you'll have to calculate the radius first. The radius is half of the diameter, so in this case:
radius = diameter/2 = 3480 km / 2 = 1740 km
Now that you have the radius, you can substitute it into the formula to find the volume.
Volume = (4/3) * π * (1740^3) km^3
Using a calculator (and π ≈ 3.14159), you can find that the volume of the Moon is approximately 2.19 × 10^10 cubic kilometers (rounded to two decimal places).
To figure out how many Moons would be needed to create a volume equal to the Earth, we need to determine the volume of the Earth as well. The process is the same, but we'll use the known diameter of the Earth, which is approximately 12,742 km.
First, calculate the radius:
radius = diameter/2 = 12,742 km / 2 = 6,371 km
Substitute the radius into the volume formula:
Volume of Earth = (4/3) * π * (6371^3) km^3
Using a calculator, the volume of the Earth is approximately 1.08 × 10^12 cubic kilometers (rounded to two decimal places).
To find how many Moons would be needed to have a volume equal to the Earth, divide the volume of the Earth by the volume of the Moon:
Number of Moons = Volume of Earth / Volume of Moon
Number of Moons = 1.08 × 10^12 km^3 / 2.19 × 10^10 km^3
After performing the division, the approximate number of Moons needed to create a volume equal to the Earth is approximately 49.37 (rounded to two decimal places).
Therefore, it would take about 49 Moons to account for the volume of the Earth.