Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water is this per hour? (Round your answer to the nearest whole number.)

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03-11-2026
Mathematics

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Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water is this per hour? (Round your answer to the nearest whole number.)

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T13:20:18-05:00

Identify the given rate: \(462 \text{ cubic inches/minute}\).
Determine conversion factors: \(1 \text{ ft}^3 = 1728 \text{ in}^3\) and \(1 \text{ hour} = 60 \text{ minutes}\).
Convert the rate: \(\frac{462 \times 60}{1728} \approx 16.04167 \text{ cubic feet/hour}\).
Round the final result: \(\boxed{16} \text{ cubic feet/hour}\).

Explanation

Analysis of the Problem and Data

We are given a water flow rate of \(462\) cubic inches per minute and need to convert this into cubic feet per hour.
First, we recall the conversion factors between these units:

There are \(12\) inches in \(1\) foot, so \(1\) cubic foot is \(12 \times 12 \times 12 = 1728\) cubic inches.
There are \(60\) minutes in \(1\) hour.

To find the rate in cubic feet per hour, we need to convert both the unit of volume and the unit of time.

Calculating the Flow Rate

We can set up the conversion expression by using the given rate and the conversion factors.
The rate \(R\) in cubic feet per hour is calculated as:
\[ R = \left( \frac{462 \text{ cubic inches}}{1 \text{ minute}} \right) \times \left( \frac{1 \text{ cubic foot}}{1728 \text{ cubic inches}} \right) \times \left( \frac{60 \text{ minutes}}{1 \text{ hour}} \right) \]
By cancelling the units of cubic inches and minutes, we get:
\[ R = \frac{462 \times 60}{1728} \text{ cubic feet per hour} \]
Performing the multiplication in the numerator:
\[ 462 \times 60 = 27720 \]
Now we divide this by the number of cubic inches in a cubic foot:
\[ R = \frac{27720}{1728} \approx 16.04167 \text{ cubic feet per hour} \]

Rounding and Final Conclusion

The calculation gives a rate of approximately \(16.04167\) cubic feet per hour. The problem requires rounding this value to the nearest whole number. Since \(0.04167\) is less than \(0.5\), we round down to \(16\).
Therefore, the flow rate is approximately \(16\) cubic feet per hour.

Examples

Understanding unit conversion is essential in many engineering and plumbing tasks. For instance, if you are designing a water irrigation system or filling a swimming pool, you often need to know how much volume is delivered over a specific period of time to ensure it meets your requirements. Converting rates helps in standardizing measurements and making informed decisions about resource management.