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, 19:38: PM
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)
r3 = (4/3)
(d/2)3 = (1/6)
d3
![begin mathsize 14px style straight pi end style](https://images.topperlearning.com/topper/tinymce/cache/df87b0d41373b1aae9f4b0b7068f8599.png)
![begin mathsize 14px style straight pi end style](https://images.topperlearning.com/topper/tinymce/cache/df87b0d41373b1aae9f4b0b7068f8599.png)
![begin mathsize 14px style straight pi end style](https://images.topperlearning.com/topper/tinymce/cache/df87b0d41373b1aae9f4b0b7068f8599.png)
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](https://images.topperlearning.com/topper/tinymce/cache/a3a396493f7c0668c97c5b42b280d1c2.png)
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](https://images.topperlearning.com/topper/tinymce/cache/0dc47b8cd151489df354e010d211d26e.png)
Hence , Volume of moon is (1/64)th of volume of earth.
Answered by Thiyagarajan K | 07 Jan, 2023, 20:12: PM
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