Question

A forest ranger wants to install a 1,500 CFM (cubic feet per minute) fan. A ranger station consists of a rectangular prism and a rectangular pyramid. The base of the pyramid and prism is 10 ft by 8 ft. The height of the pyramid is 3 ft and the height of the prism is 8 ft. The ranger station requires one CFM per ft2. Will the fan provide enough airflow for the ranger station? Why or why not?

Answer 1

Sample response: Yes, the fan will provide enough airflow. The volume of the ranger station is 720 cubic feet. The ranger station requires a 720 CFM fan. 1,500 CFM is greater than 720 CFM, so it will be enough airflow.

Answer 2

Yes, fan will provide enough airflow in the ranger station.

Explanation:

A ranger station consist of a rectangular pyramid and a rectangular prism.

So volume of air in ranger station = volume of prism + volume of a pyramid

Volume of a rectangular prism = Length×Width×height

= 10×8×8 = 640 ft³

Volume of the pyramid =
`(1)/(3)(\text{area of the base)(height)}`

=
`(1)/(3)(10)(8)(3)`

= 80 ft³

Total volume of the ranger station = 640 + 80 = 720 ft³

Since CFM has the airflow capacity of 1500 cubic feet per minute so one CFM will be sufficient for the volume of 720 ft³.