To convert the flow rate from cubic inches per minute to cubic feet per hour, we will follow these steps:
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Convert cubic inches to cubic feet: There are 12 inches in a foot, so: \[ 1 \text{ cubic foot} = 12 \times 12 \times 12 = 1728 \text{ cubic inches} \] Thus, to convert cubic inches to cubic feet, divide by 1728.
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Calculate the flow in cubic feet per minute: \[ \text{Flow in cubic feet per minute} = \frac{462 \text{ cubic inches}}{1728 \text{ cubic inches per cubic foot}} = \frac{462}{1728} \approx 0.267 \]
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Convert minutes to hours: Since there are 60 minutes in an hour: \[ \text{Flow in cubic feet per hour} = 0.267 \text{ cubic feet per minute} \times 60 \text{ minutes per hour} \approx 16.02 \]
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Round to the nearest whole number: \[ 16.02 \approx 16 \]
Therefore, the flow rate of water is approximately \( \boxed{16} \) cubic feet per hour.