EXAMPLE 2.7.5

The radius of the Earth is about 4000 miles. The radius of the Sun is about 400,000 miles. How many times bigger than the Earth is the Sun?

A. 10

B. 100

C. 1,000

D. 1,000,000

SOLUTION

To compare the size of the Earth with the size of the Sun we can divide the volume of the Earth into the volume of the Sun. This will tells us how many Earths would "fit into" the Sun.

We use the following formula to find the volume of a sphere:

Volume = (four thirds) times pi times (radius cubed)

The volume of the Earth, with its 4,000 mile radius, is

Volume = (four thirds) times pi times (4,000 cubed) or 2.68 times 10 to the eleventh power cubic miles.

The volume of the Sun, with its radius of 400,000 miles, is

Volume = (four thirds) times pi times (400,000 cubed) or 2.68 times 10 to the seventeenth power cubic miles.

Now divide the volume of the Sun by the volume of the earth:

(2.68 times 10 to the eleventh power) divided by (2.68 times 10 to the seventeenth power) = 1 times 10 to the sixth power, or 1 million.

The Sun is about one million times the size of the Earth; that is, if it were hollow the Sun could contain roughly 1,000,000 Earths.