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

Let diameter of the Earth `= d_(1)`
Then, diameter of the Moon `= (1)/(4)d_(1)`
`therefore` radius of the Earth, `r_(1)=(d_(1))/(2)`
Radius of the Moon, `r_(2)=(d_(1))/(2xx4)=(d_(1))/(8)`
Surface area of the Earth `= 4pi r_(1)^(2)`
`S_(1)=4pi ((d_(1))/(2))^(2)=pid_(1)^(2)`
Surface area of the Moon `= 4pi((d_(1))/(8))^(2)=4pi (d_(1)^(2))/(64)`
`S_(2)=(pi d_(1)^(2))/(16)`
Hence, `S_(1) : S_(2) = (pi d_(1)^(2))/(1) : (pi d_(1)^(2))/(16)`
`rArr S_(1) : S_(2) = 16 : 1`