An architect uses a 3-D printer to create the scale model for a house that will be built. In the model the house is 53cm tall. The house will be 624 cm tall. The volume of the model is 0.8125 cubic meter. What is the volume of the house. (Note: 1 cubic meter = 1,000,000 cubic centimeters)

The volume of the actual house is 1,324.94 cubic meters

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Height of the scale model = 53 cm

Height of the actual house = 624 cm

Scale of the model = 642/53 = 11.77

Volume of the scale model = 0.8125 cubic meters

2. What is the volume of the house?

For answering the question we have to find the width and the length of the model, then use the scale of the model for calculating the volume of the actual house, this way:

Volume of the scale model = 0.8125 cubic meters

Area of the scale model = Volume of the model/Height of the model

Area of the scale model = 0.8125/0.53

Area of the scale model = 1.533 square meters

Area of the scale model = Length * Width

Area of the scale model = 1.533 * 1

Now, we can calculate, the measurements of the house to calculate its volume:

Height of the actual house = 6.24 meters

Length of the actual house = 1.533 * 11.77 = 18.04 meters

Width of the actual house = 1 * 11.77 = 11.77 meters

Volume of the actual house = 6.24 * 18.04 * 11.77

Volume of the actual house = 1,324.94 cubic meters