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CBSE Class 9 Answered

the diameter of 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?
Asked by rajeshporwal02 | 07 Jan, 2023, 07:38: PM
answered-by-expert Expert Answer
Let us assume earth and moon are spherical in shape.
 
Let r be radius and d be diameter of sphere
 
Volume of sphere V = (4/3)begin mathsize 14px style straight pi end styler3 = (4/3)begin mathsize 14px style straight pi end style(d/2)3 = (1/6)begin mathsize 14px style straight pi end styled3
 
Volume is proportional to cube of diameter.
 
Let VE be volume of earth and dE is its diameter.
 
Let VM be volume of moon and dM is its diameter.
 
begin mathsize 14px style V subscript M over V subscript E space equals space open parentheses d subscript M over d subscript E close parentheses cubed end style
 
dM = (1/4) dE   ( given )
 
begin mathsize 14px style V subscript M over V subscript E space equals space open parentheses 1 fourth close parentheses cubed space equals space 1 over 64 end style
 
Hence , Volume of moon is (1/64)th of volume of earth.
 
 

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