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?

Answer

`(1)/(64)`

Explanation

`d = (1)/(4) D rArr 2r = (1)/(4) xx 2R rArr r = (1)/(4)R`
Volume of moon `= (4)/(3) pi r^(3) = (4)/(3) pi ((R)/(4))^(3) = ((4)/(3) pi R^(3))/(64)`
Volume of earth `= (4)/(3) pi R^(3)`
`:.` volume of moon `= (1)/(64) xx` volume of earth