A building in the shape of a cube has a width of 30ft a length of 30ft and a height of 30ft. An architect wants to build a scale model of the building that is 10% smaller in volume. What is the height of the new building? Round to the nearest hundredth.

The height of the scale model is 13.92 feet. (Rounding to the nearest hundredth).

Step-by-step explanation:

These are the measurements of the real building:

Height = 30 feet

Width = 30 feet

Length = 30 feet

Volume of the real building = 30 * 30 * 30 = 27,000 cubic feet

These are the measurements of the scale model:

Volume of the scale model = 10% of 27,000 cubic feet

Volume of the scale model = 0.1 * 27,000 = 2,700 cubic feet

Height = ∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)

Width = ∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)

Length = ∛ 2,700 = 13.92 feet (Rounding to nearest hundredth)

The height of the scale model is 13.92 feet.