Question

A building in the shape of a cube has a width of 30 ft., a length of 30 ft., and a height of 30 ft. 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?

Answer 1

28,96 ft (round to the nearest hundreds)

Explanation:

1) find the volume of the first cube

V = side^3 = 30^3 = 27000 ft^3

2) find the 10% of 27000

27000 / 0,1 = 2700

3) find the volume of the second cube

V = 27000- 2700 = 24300 ft^3

4) find the height

height = ∛24300 = 28,96 ft (round to the nearest hundreds)

Answer 2

Explanation:

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

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.