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?

Let, the radius of Earth be R
Therefore, the diameter of Earth = 2R
According to question, diameter of moon = 1/4(2R)
So, the radius of moon = 1/4(2R)/2 = (1/4)R
Volume of moon/Volume of Earth = 4/3π(1/4R)³/4/3π(R)³ = 1/64R³/R³ = 1/64
⇒ Volume of moon = 1/64 × volume of Earth
Hence, the volume of moon is 1/64 the volume of Earth.