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

Ex 13.8, 4 - Chapter 13 Class 9 Surface Areas and Volumes - Part 2
Ex 13.8, 4 - Chapter 13 Class 9 Surface Areas and Volumes - Part 3

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Ex 11.4 , 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 = π‘₯/4 Hence, Radius of earth = π‘₯/2 & Radius of moon = 1/2Γ—π‘₯/4 = π‘₯/8 Now, (π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘šπ‘œπ‘œπ‘›)/(π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘’π‘Žπ‘Ÿπ‘‘β„Ž) = (4/3 πœ‹(π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ π‘šπ‘œπ‘œπ‘›)^3)/(4/3 πœ‹(π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ π‘’π‘Žπ‘Ÿπ‘‘β„Ž)^3 ) = (π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ π‘šπ‘œπ‘œπ‘›)^3/(π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ π‘’π‘Žπ‘Ÿπ‘‘β„Ž)^3 = (π‘₯/8)^3/(π‘₯/2)^3 = (π‘₯^3/8^3 )/(π‘₯^3/2^3 ) = π‘₯^3/8^3 Γ— 2^3/π‘₯^3 = 2^3/8^3 = (2 Γ— 2 Γ— 2)/(8 Γ— 8 Γ— 8) = 1/(4 Γ— 4 Γ— 4) = 1/64 ∴ (π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘šπ‘œπ‘œπ‘›)/(π‘‰π‘œπ‘™π‘’π‘šπ‘’ π‘œπ‘“ π‘’π‘Žπ‘Ÿπ‘‘β„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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.