What is 34.7 inches of rainfall over 1700 square feet converted to gallons of water?
Understand the Problem
The question requires converting a volume of rainfall given in inches over a square footage area into gallons. To solve this, we need to convert inches of rainfall and square feet into cubic feet, then convert cubic feet to gallons.
Answer
$\text{Volume in gallons} = \text{Area in square feet} \times \frac{\text{Rainfall in inches}}{12} \times 7.48$
Answer for screen readers
The solution requires the rainfall in inches and the area in square feet to be provided. Assuming that we have 1 inch of rainfall over 1 square foot, we can calculate the volume in gallons:
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Convert inches to feet: $\text{Rainfall in feet} = \frac{1}{12} \text{ feet}$
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Calculate the volume of rainfall in cubic feet: $\text{Volume in cubic feet} = 1 \text{ square feet} \times \frac{1}{12} \text{ feet} = \frac{1}{12} \text{ cubic feet}$
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Convert cubic feet to gallons: $\text{Volume in gallons} = \frac{1}{12} \text{ cubic feet} \times 7.48 \frac{\text{gallons}}{\text{cubic feet}} \approx 0.623 \text{ gallons}$
Steps to Solve
- Convert inches to feet
To convert inches to feet, divide the number of inches by 12 since there are 12 inches in a foot.
$ \text{Rainfall in feet} = \frac{\text{Rainfall in inches}}{12} $
- Calculate the volume of rainfall in cubic feet
Multiply the area in square feet by the rainfall in feet to find the volume in cubic feet.
$ \text{Volume in cubic feet} = \text{Area in square feet} \times \text{Rainfall in feet} $
- Convert cubic feet to gallons
Multiply the volume in cubic feet by the conversion factor of approximately 7.48 gallons per cubic foot.
$ \text{Volume in gallons} = \text{Volume in cubic feet} \times 7.48 $
The solution requires the rainfall in inches and the area in square feet to be provided. Assuming that we have 1 inch of rainfall over 1 square foot, we can calculate the volume in gallons:
-
Convert inches to feet: $\text{Rainfall in feet} = \frac{1}{12} \text{ feet}$
-
Calculate the volume of rainfall in cubic feet: $\text{Volume in cubic feet} = 1 \text{ square feet} \times \frac{1}{12} \text{ feet} = \frac{1}{12} \text{ cubic feet}$
-
Convert cubic feet to gallons: $\text{Volume in gallons} = \frac{1}{12} \text{ cubic feet} \times 7.48 \frac{\text{gallons}}{\text{cubic feet}} \approx 0.623 \text{ gallons}$
More Information
There are approximately 7.48 gallons in a cubic foot. This conversion factor is essential for converting volumes from cubic feet to gallons.
Tips
A common mistake is forgetting to convert inches to feet before calculating the volume in cubic feet. Ensure all units are consistent (i.e., all in feet) before multiplying to find the volume. Another mistake is using an incorrect conversion factor between cubic feet and gallons.
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