You are a project manager and you must build a new academic building for the university in the shape of a rectangular prism. The building (rectangular prism) is as wide as it is tall. The roof is in the shape of a triangular prism. The total height of the building is 40 feet tall and 100 feet long. The height of the triangular prism that forms the roof must be at least 5 feet tall (could be taller than 5 feet).

1. Draw a diagram that indicates all the dimensions of the building.

2. Find an equation that represents the volume of the building.

3. You must install a heating and air conditioning unit. In order to install the correct unit you must find the volume of the building. Find a function that models the volume of the building in terms of the width of the building.

4. What is the domain of the function?