How many gallons of water is in 0.17 inches of rain?
Understand the Problem
The question asks how to convert a rainfall measurement (0.17 inches) into gallons of water. This requires understanding the area over which the rain falls, as the volume of water depends on both the depth of the rainfall and the area. Since the area isn't specified, we will assume a standard area such as a square foot or an acre to provide an example calculation.
Answer
For 1 square foot: $0.106$ gallons For 1 acre: $4617.36$ gallons
Answer for screen readers
For 1 square foot: $0.106$ gallons
For 1 acre: $4617.36$ gallons
Steps to Solve
- Choose an area
Since the area is not provided, let's calculate for an area of 1 square foot for simplicity. We will later scale this up to an acre.
- Convert inches to feet
Convert the rainfall from inches to feet by dividing by 12, as there are 12 inches in a foot.
$$ 0.17 \text{ inches} \div 12 \frac{\text{inches}}{\text{foot}} = 0.01416667 \text{ feet} $$
- Calculate the volume in cubic feet
The volume of water is the area multiplied by the rainfall depth. Since we're using 1 square foot as the area:
$$ \text{Volume} = \text{Area} \times \text{Depth} = 1 \text{ ft}^2 \times 0.01416667 \text{ ft} = 0.01416667 \text{ ft}^3 $$
- Convert cubic feet to gallons
Convert the volume from cubic feet to gallons. There are approximately 7.48 gallons in a cubic foot.
$$ 0.01416667 \text{ ft}^3 \times 7.48 \frac{\text{gallons}}{\text{ft}^3} = 0.106 \text{ gallons} $$ This is the amount of rain, in gallons, that falls on one square foot.
- Calculate the volume in gallons for one acre
One acre is equal to 43,560 square feet. Multiply the rainfall in gallons per square foot by the number of square feet in an acre.
$$ 0.106 \frac{\text{gallons}}{\text{ft}^2} \times 43560 \text{ ft}^2 = 4617.36 \text{ gallons} $$ Therefore, 0.17 inches of rainfall over one acre is approximately 4617.36 gallons.
For 1 square foot: $0.106$ gallons
For 1 acre: $4617.36$ gallons
More Information
The conversion factor from cubic feet to gallons is approximately 7.48. This value is commonly used in various hydrological and engineering calculations.
Tips
A common mistake is forgetting to convert inches to feet before calculating the volume. Also, using an incorrect conversion factor between cubic feet and gallons is another common mistake. Always double-check the units and conversions.
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