Answer: The volume of air in the building is [tex]980 ft^{3}[/tex]
Step-by-step explanation:
The attached image shows the shape of the building and the described dimensions.
As we can see, the building is a combanation of a triangular prism and a parallelepiped. So, we have to calculate the volume in both figures and sum the total to obtain the whole volume.
The volume of a Triangular prism is the area of the triangle multiplied by the height of the prism:
[tex]V_{prism}=(\frac{(b)(h)}{2})H[/tex] (1)
Where:
[tex]b=4 ft[/tex] is the base of thee triangle
[tex]h=15 ft-9.5 ft=5.5 ft[/tex] is the height of thee triangle
[tex]H=20 ft ft[/tex] is the height of triangular prism
Then:
[tex]V_{prism}=(\frac{(4 ft)(5.5 ft)}{2})20 ft[/tex] (2)
[tex]V_{prism}=220 ft^{3}[/tex] (3)
The volume of a parallelepiped is the area of the rectangle multiplied by the height:
[tex]V_{parallelepiped}=(L)(W)(A)[/tex] (4)
Where:
[tex]L=20 ft[/tex] is the length
[tex]W=4 ft[/tex] is the width
[tex]A=9.5 ft[/tex] is the height
[tex]V_{parallelepiped}=(20 ft)(4 ft)(9,5 ft)[/tex] (5)
[tex]V_{parallelepiped}=760 ft^{3}[/tex] (6)
Now, the total volume is:
[tex]V_{prism}+V_{parallelepiped}=220 ft^{3}+760 ft^{3}[/tex] (7)
[tex]V_{prism}+V_{parallelepiped}=980 ft^{3}[/tex] This is the volume of air in the building
