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?

Solution:

Let the diameter of earth be “d”. Therefore, the radius of earth will be will be d/2

Diameter of moon will be d/4 and the radius of moon will be d/8

Find the volume of the moon :

Volume of the moon = (4/3) πr3 = (4/3) π (d/8)3 = 4/3π(d3/512)

Find the volume of the earth :

Volume of the earth = (4/3) πr3= (4/3) π (d/2)3 = 4/3π(d3/8)

Fraction of the volume of the earth is the volume of the moon

Answer: Volume of moon is of the 1/64 volume of earth.