What Is the Volume of the Earth?

If you could drop the earth into a graduated cylinder filled with water, the amount of water displaced by the earth would be equal to its volume. Since we can't do that, we have to rely on sophisticated mathematical formulas to discover the volume of the earth. Because the earth is a sphere, we can use the formula for the volume of a sphere to figure out the earth's volume.

History

Archimedes, a Greek mathematician, derived the formula for the volume of a sphere to be 4 divided by 3 times the sphere's radius cubed times pi. Pi, symbolized by this letter of the Greek alphabet, is equal to 3.141. To find the values of the other variable, we need to know the earth's radius. Actually, you can use the same formula for any ball or sphere if you know the radius. Obviously, the volume of the earth will be a very large number.

Significance

A radius is always one-half the length of the diameter or the distance from a point one side of the sphere or circle to a point at the opposite side going through the exact center. It is like a spoke in a wheel that connects the rim with the center. The earth's radius is so large that we have to use scientific notation to express its length. It is 6 times 10 raised to the sixth power meters long. Writing it out, the radius of the earth equals 6,000,000 meters in length. According to Think-Metric, 1,000 meters is the same as the height of three stacked up Chicago Sears Towers. So, if you piled 18,000 Sears Towers on top of each other and measured the total height of the new building, it would equal the radius of the earth.

Effects

Using Archimedes' formula for the volume of a sphere and the value of the radius of the earth, we can determine the volume of the earth itself to be 10 (raised to the 21st power) times 1.1 meters cubed. This number is so large that it is easiest to understand when it is expressed in scientific notation. Written out long-hand, the number that tells the exact volume of the earth looks like this: 1,100,000,000,000,000,000,000 meters cubed.

Size

These numbers are so large that we have a lot of difficulty envisioning them. It may help to know the volume of some familiar smaller things. A railroad tank car has a volume of 10 to the second power. A cup has a volume of 10 to the negative fourth power. The number which expresses the volume of the earth ends with more than 19 more zeros than the volume of a tank car.

Benefits

In effect, the volume of the earth tells us how much space the planet takes up. Knowing the volume of the earth can help geophysicists predict the rate at which heat from the earth's crust will be released to the surface. This rate is figured as temperature released unit of volume. In general, though, most people will never need to know the volume of the earth unless it comes up in a trivia contest.

Resources

• Facts About Earth
• Comparing the Volumes of the Earth, Jupiter, and the Sun