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?

Explanation

The volume of a sphere of base radius `r` is `4/3 (pi) r^3`
Let the radius of the earth be `R` and the radius of the moon be `r`
Diameter of the moon `= 1/4 xx ` diameter of the earth
The radius of the moon `= 1/4 ×` radius of the earth [Since, diameter` = 2 xx `Radius]
`r = 1/4 xx R`
`r = R/4`
The volume of the earth `= 4/3 (pi)R^3`
The volume of the moon `= 4/3 (pi) r^3`
`= 4/3 (pi) (R/4)^3` [ replacing `r` with `R/4` ]
`= 1/64 xx 4/3 (pi)R^3`
The volume of the moon `= 1/64 xx ` Volume of the earth
Hence the volume of the moon is `1/64` times the volume of the earth.