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 diameter of earth be d. Therefore, the radius of earth will be d/2.
Diameter of moon will be d/4 and the radius of moon will be d/8.
`"Volume of moon "=4/3pir^3=4/3pi(d/8)^3=1/512xx4/3pid^3`
`"Volume of earth "=4/3pi^3=4/3pi(d/2)^3=1/8xx4/3pid^3`
`"Volume of moon"/"Volume of earth"=(1/512xx4/3pid^3)/(1/8xx4/3pid^3)=1/64`
`rArr "Volume of moon "=1/64"Volume of earth"`
Therefore, the volume of moon is 1/64 of the volume of earth.
The diameter of the moon is approximately one fourth of the diameter of the earth.
Let diameter of earth bed. So radius =`d/2`
Then, diameter of moon`=d/4,radius =2/4=d/8`
Volume of moon `=4/3πr^3=4/3π(d/8)^3=4/3xx1/512πd^3`
Volume of earth `=4/3πr^3=4/3π(d/2)^3=1/8xx4/3πd^3`
`"Volume of moon"/"Volume of earth"=(1/512xx4/3πd^3)/(1/8xx4/3πd^3)=1/64`
Thus, the volume of moon is `1/64`of volume of earth.
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