Question

A building contractor needs to compute the volume of air contained in a building with a rectangular floor, as shown in the figure below. The building is 20 feet long, 4 yards wide, 9
1
2
feet high on two sides 9 and a half feet high on two sides and 15 feet high from the floor to the peak. What is the volume of air in the building in cubic feet?

Answer 1

Answer: The volume of air in the building is $980 ft^{3}$

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:

$V_{prism}=(\frac{(b)(h)}{2})H$ (1)

Where:

$b=4 ft$ is the base of thee triangle

$h=15 ft-9.5 ft=5.5 ft$ is the height of thee triangle

$H=20 ft ft$ is the height of triangular prism

Then:

$V_{prism}=(\frac{(4 ft)(5.5 ft)}{2})20 ft$ (2)

$V_{prism}=220 ft^{3}$ (3)

The volume of a parallelepiped is the area of the rectangle multiplied by the height:

$V_{parallelepiped}=(L)(W)(A)$ (4)

Where:

$L=20 ft$ is the length

$W=4 ft$ is the width

$A=9.5 ft$ is the height

$V_{parallelepiped}=(20 ft)(4 ft)(9,5 ft)$ (5)

$V_{parallelepiped}=760 ft^{3}$ (6)

Now, the total volume is:

$V_{prism}+V_{parallelepiped}=220 ft^{3}+760 ft^{3}$ (7)

$V_{prism}+V_{parallelepiped}=980 ft^{3}$ This is the volume of air in the building