Melting a metal ball of radius 3 units, 27 identical dice and a ball of radius 1 units are made. What is the side of dice?
The volume of the original metal ball =4/3 π (3)3 = 36 π cubic units The volume of the smaller ball =4/3 π (1)3 =4 π /3 cubic units The total volume of the metal used is equal to the volume of the original ball minus the volume of the smaller ball: Vtotal=36 π -4 π/3 = (108 π-4 π)/3 =104π/3 There are 27 identical dice, so the volume of each die is: = Total volume /27 = (104π/3)/27 =104π/81 = (104×3.14)/81 =4.03 cubic units The volume of a cube with side length a is: a3 =4.03 a =1.6 (Approx)
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