Question

If the earth is bigger than the moon by 25 times, how big is the moon? Express your answer in scientific notation.

Answer 1

The Solution:

The radius of the earth (R) = 6378 kilometers.

Comparing the size of the earth to that of the moon by their volumes

We have the volume of the earth as below:

Assumption: The earth is spherical.

`V=(4\pi r^3)/(3)`

In this case,

r=radius of the earth =6378km

V=volume of the earth =?

Substituting these values in the formula, we get

`V=(4\pi(6378)^3)/(3)=(1.086781293*10^(12))km^3`

To find how big the moon is, we shall divide the volume of the earth by 25 since the earth is bigger than the moon by 25 times.

`\text{ Volume of the moon = }(4\pi(6378)^3)/(3*25)=(4.34712517*10^(10))km^3`

Therefore, the correct answer is

`(4.34712517*10^(10))km^3`