Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. what fraction of the volume of the earth is the volume of the moon?

a. 1/4
b. 1/16
c. 1/64
d. 1/256

Answer 1

The volume of the Moon is 1/64 the volume of the Earth because volume is proportional to the cube of the diameter, and the Moon's diameter is one-fourth that of the Earth.

Step-by-step explanation:

If the diameter of the Moon is approximately one-fourth of the diameter of the Earth, we need to understand how this affects their volumes to find the fraction of the volume of the Earth that is the volume of the Moon. Since volume is proportional to the cube of the diameter, you must cube the ratio of their diameters to find the ratio of their volumes. Therefore, we cube (1/4) to get:

(1/4) ³ = (1³)/(4³) = 1/64.

So, the volume of the Moon is 1/64 the volume of the Earth, which means the correct answer is c. 1/64.