A room measures 38' x 38' x 10' high. How many air changes per hour occur (ACH) if 55,920 cubic feet of air enters and leaves the room each hour?

To determine the number of air changes per hour (ACH), it is crucial to first calculate the volume of the room. The dimensions provided are 38 feet in length, 38 feet in width, and 10 feet in height.

The volume of the room can be calculated using the formula for the volume of a rectangular prism:

[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} ]

[ \text{Volume} = 38' \times 38' \times 10' = 14,440 \text{ cubic feet} ]

Next, to find the ACH, the formula is:

[ \text{ACH} = \frac{\text{Volume of air entering or leaving the room (cubic feet per hour)}}{\text{Volume of the room (cubic feet)}} ]

Using the values calculated and given:

[ \text{ACH} = \frac{55,920 \text{ cubic feet per hour}}{14,440 \text{ cubic feet}} ]

When you perform the division:

[ \text{ACH} = \frac{55,920}{14,440} \approx 3.87