4. In order to properly design a heating system for a greenhouse, the volume of air in the building needs to be determined. Find the volume of air in the greenhouse below. The length of the building is 40 feet long, the width is 20 feet long, and it is 8 feet from the ground to the gable. For the triangular prism on top, the height of the triangle is 7 feet
To find the volume of air in the greenhouse, you need to calculate the volume of the rectangular base and the volume of the triangular prism on top separately, and then add them together.
1. Calculate the volume of the rectangular base:
The volume of a rectangular prism (V) is calculated using the formula: V = length x width x height.
In this case, the length (L) is 40 feet, the width (W) is 20 feet, and the height (H) is 8 feet from the ground to the gable.
So, the volume of the rectangular base is: V_rectangular_base = L x W x H.
2. Calculate the volume of the triangular prism on top:
The volume of a prism (V) is calculated using the formula: V = base area x height.
The base area of a triangle is calculated using the formula: Base Area = 0.5 x base x height.
In this case, the base (B) of the triangle is the length of the building (40 feet), and the height (H) of the triangle is given as 7 feet.
So, the base area (A) of the triangle is: A = 0.5 x B x H = 0.5 x 40 ft x 7 ft.
Then, the volume of the triangular prism is: V_triangular_prism = A x H.
3. Add the volumes together to get the total volume of air in the greenhouse:
Total Volume = V_rectangular_base + V_triangular_prism.
To solve this problem, substitute the given values into the formulas and perform the calculations.