Question

A building has a volume of 410,100 cubic feet. A model of the building is made with a scale factor of 1/40. To the nearest hundredth of a cubic foot, what is the volume of the model?

Answer 1

To find the volume of the model, we need to multiply the volume of the actual building by the cube of the scale factor, since the scale factor applies to all three dimensions (length, width, and height).

The scale factor is 1/40, so its cube is (1/40)^3 = 1/64,000. Multiplying this by the volume of the actual building (410,100 cubic feet):

Volume of the model = (1/64,000) * 410,100 cubic feet

Calculating this value gives us approximately 6.42 cubic feet for the volume of the model, rounded to the nearest hundredth.