Chapter 13 Class 9 Surface Areas and Volumes (Term 2)

Serial order wise

Last updated at March 6, 2017 by Teachoo

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 = π₯/4 Hence, Radius of earth = π₯/2 & Radius of moon = 1/2Γπ₯/4 = π₯/8 Now, (ππππ’ππ ππ ππππ)/(ππππ’ππ ππ ππππ‘β) = (4/3 π(π ππππ’π ππ ππππ)^3)/(4/3 π(π ππππ’π ππ ππππ‘β)^3 ) = (π ππππ’π ππ ππππ)^3/(π ππππ’π ππ ππππ‘β)^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 β΄ (ππππ’ππ ππ ππππ)/(ππππ’ππ ππ ππππ‘β) = 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.