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प्रश्न
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?
उत्तर
Let the diameter of the earth be d. Therefore, the radius of the earth will be `d/2`.
The diameter of the moon will be `d/4`, and the radius of the moon will be `d/8`.
Volume of the moon = `4/3pir^3=4/3pi(d/8)^3=1/512xx4/3pid^3`
Volume of the earth = `4/3pi^3=4/3pi(d/2)^3=1/8xx4/3pid^3`
`"Volume of the moon"/"Volume of the earth"` = `(1/512xx4/3pid^3)/(1/8xx4/3pid^3) = 1/64`
⇒ Volume of the moon = `1/64 "Volume of the earth"`
Therefore, the volume of the moon is `1/64` of the volume of the earth.
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