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Answer :
Certainly! Let's carefully convert 20,000 cubic feet (ft³) to gallons (gal) using the given table and dimensional analysis.
### Step-by-Step Solution
1. Identify the Conversion Factor:
From the table, we know that:
[tex]\[
1 \text{ cubic foot} = 7.48 \text{ gallons}
\][/tex]
2. Set Up the Conversion:
To convert 20,000 cubic feet to gallons, we use the conversion factor:
[tex]\[
20,000 \text{ cubic feet} \times \frac{7.48 \text{ gallons}}{1 \text{ cubic foot}}
\][/tex]
3. Perform the Multiplication:
[tex]\[
20,000 \text{ cubic feet} \times 7.48 \frac{\text{gallons}}{\text{cubic foot}} = 149,600 \text{ gallons}
\][/tex]
4. Round to the Nearest Hundredth (if necessary):
Although our multiplication gives us 149,600 gallons exactly, if needed, rounding to the nearest hundredth would still result in:
[tex]\[
149,600.00 \text{ gallons}
\][/tex]
Therefore, the final answer to convert 20,000 cubic feet to gallons is:
[tex]\[
149,600 \text{ gallons}
\][/tex]
### Step-by-Step Solution
1. Identify the Conversion Factor:
From the table, we know that:
[tex]\[
1 \text{ cubic foot} = 7.48 \text{ gallons}
\][/tex]
2. Set Up the Conversion:
To convert 20,000 cubic feet to gallons, we use the conversion factor:
[tex]\[
20,000 \text{ cubic feet} \times \frac{7.48 \text{ gallons}}{1 \text{ cubic foot}}
\][/tex]
3. Perform the Multiplication:
[tex]\[
20,000 \text{ cubic feet} \times 7.48 \frac{\text{gallons}}{\text{cubic foot}} = 149,600 \text{ gallons}
\][/tex]
4. Round to the Nearest Hundredth (if necessary):
Although our multiplication gives us 149,600 gallons exactly, if needed, rounding to the nearest hundredth would still result in:
[tex]\[
149,600.00 \text{ gallons}
\][/tex]
Therefore, the final answer to convert 20,000 cubic feet to gallons is:
[tex]\[
149,600 \text{ gallons}
\][/tex]
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