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.

$V=\frac{4\pi r^3}{3}$

In this case,

r=radius of the earth =6378km

V=volume of the earth =?

Substituting these values in the formula, we get

$V=\frac{4\pi(6378)^3}{3}=(1.086781293\times10^{12})km^3$

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.

$\text{ Volume of the moon = }\frac{4\pi(6378)^3}{3\times25}=(4.34712517\times10^{10})km^3$

Therefore, the correct answer is

$(4.34712517\times10^{10})km^3$