A miniature model for a sculpture weighs 10 ounces and stands 8 inches high. The actual model is to be 3 feet high and weigh over 25 pounds. Can it be made from the same material as the model? If not, how should its weight per cubic inch compare to that of the model material?
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The height increases by a factor of 4.5, and so do the width and the depth. All three dimensions of the three-dimensional sculpture increase by the same factor. The volume increases by 4.4 x 4.5 x 4.5 = 4.53, or 91.125.
The weight of the sculpture depends on the volume and the weight per cubic inch. We don’t know the volume of the model, but we do know that the volume is 91.125 times the volume of the model, so the weight of the sculpture is 91.125 times the weight of the model...
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