A cubical block of wood weighs 5 kilograms. How much will another cube of the same wood weigh if its sides are three times as long?
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The correct answer is E.
Weight is proportional to volume.
Volume of a cube = (one side)\(^3\)
Let x be the side of the first cube. So:
Volume \(= x^3\)
The sides of the second cube are three times as long. So:
Volume \(= (3x)^3 = 27x^3\)
The ratio of the volumes of the old and new cubes will be 1: 27. So, if the first weighs 5 kilograms, the second weighs 27 × 5 kilograms =135 kilogram.
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