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 ft³. will the fan provide enough airflow for the ranger station?
no, the fan will not provide enough airflow because 880 cfm is less than 1,500 cfm.
no, the fan will not provide enough airflow because 720 cfm is less than 1,500 cfm.
yes, the fan will provide enough airflow because 1,500 cfm is greater than 720 cfm.
yes, the fan will provide enough airflow because 1,500 cfm is greater than 880 cfm.

Explanation:

Step1: Calculate the volume of the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 10\) ft, \(w = 8\) ft, \(h = 8\) ft. So \(V_{prism}=10\times8\times8 = 640\) \(ft^{3}\).

Step2: Calculate the volume of the rectangular pyramid

The volume formula for a rectangular pyramid is \(V=\frac{1}{3}\times l\times w\times h\). Here, \(l = 10\) ft, \(w = 8\) ft, \(h = 3\) ft. So \(V_{pyramid}=\frac{1}{3}\times10\times8\times3=80\) \(ft^{3}\).

Step3: Calculate the total volume of the ranger station

The total volume \(V = V_{prism}+V_{pyramid}\). Substitute the values: \(V=640 + 80=720\) \(ft^{3}\).

Step4: Compare the fan's CFM with the required CFM

Since the ranger station requires one CFM per \(ft^{3}\), it needs 720 CFM. The fan has 1500 CFM. And \(1500>720\).

Answer:

Yes, the fan will provide enough airflow because 1,500 CFM is greater than 720 CFM.