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Ex 13.8, 4 - The diameter of the moon is approximately - Ex 13.8

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Ex 13.8 , 4 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 diameter of earth = x So, diameter of moon = ๐‘ฅ/4 Hence, Radius of earth = ๐‘ฅ/2 & Radius of moon = 1/2ร—๐‘ฅ/4 = ๐‘ฅ/8 Now, (๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘œ๐‘“ ๐‘š๐‘œ๐‘œ๐‘›)/(๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘œ๐‘“ ๐‘’๐‘Ž๐‘Ÿ๐‘กโ„Ž) = (4/3 ๐œ‹(๐‘…๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘“ ๐‘š๐‘œ๐‘œ๐‘›)^3)/(4/3 ๐œ‹(๐‘…๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘“ ๐‘’๐‘Ž๐‘Ÿ๐‘กโ„Ž)^3 ) = (๐‘…๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘“ ๐‘š๐‘œ๐‘œ๐‘›)^3/(๐‘…๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘“ ๐‘’๐‘Ž๐‘Ÿ๐‘กโ„Ž)^3 = (๐‘ฅ/8)^3/(๐‘ฅ/2)^3 = (๐‘ฅ^3/8^3 )/(๐‘ฅ^3/2^3 ) = ๐‘ฅ^3/8^3 ร— 2^3/๐‘ฅ^3 = 2^3/8^3 = (2 ร— 2 ร— 2)/(8 ร— 8 ร— 8) = 1/(4 ร— 4 ร— 4) = 1/64 โˆด (๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘œ๐‘“ ๐‘š๐‘œ๐‘œ๐‘›)/(๐‘‰๐‘œ๐‘™๐‘ข๐‘š๐‘’ ๐‘œ๐‘“ ๐‘’๐‘Ž๐‘Ÿ๐‘กโ„Ž) = 1/64 Volume of moon = 1/64 (Volume of earth) Hence, the volume of the earth is 1/64 of the volume of the earth.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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