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 ft. Will the fan provide enough airflow for the ranger station? Why or why not?

Answer:

Yes, the fan will provide enough airflow. To find the volume of the station, calculate the volume of the rectangular prism (10 * 8 * 8 = 640 cubic feet) and the volume of the rectangular pyramid (1/3 * 80 * 3 = 80 cubic feet). The total volume is 640 + 80 = 720 cubic feet. Since 1 CFM is required per cubic foot, the station requires 720 CFM. The 1,500 CFM fan is more than enough because 1,500 is greater than 720.