Convert 77 fluid ounces into cubic feet. Round your answer to the nearest hundredth.
Convert 77 fluid ounces into cubic feet. Round your answer to the nearest hundredth.
The Correct Answer and Explanation is:
Answer:
77 fluid ounces = 0.08 cubic feet (rounded to the nearest hundredth)
Explanation
To convert 77 fluid ounces into cubic feet, we must go through a series of unit conversions using known volume relationships. Fluid ounces and cubic feet both measure volume, but in different systems and scales.
Step 1: Convert fluid ounces to cubic inches
In the U.S. customary system:
- 1 fluid ounce = 1.80469 cubic inches
So: 77 fl oz×1.80469 in3fl oz=138.76013 in377 \, \text{fl oz} \times 1.80469 \, \frac{\text{in}^3}{\text{fl oz}} = 138.76013 \, \text{in}^3
Step 2: Convert cubic inches to cubic feet
In the U.S. customary system:
- 1 cubic foot = 12 × 12 × 12 = 1,728 cubic inches
So: 138.76013 in3÷1728 in3ft3=0.08027 ft3138.76013 \, \text{in}^3 \div 1728 \, \frac{\text{in}^3}{\text{ft}^3} = 0.08027 \, \text{ft}^3
Step 3: Round to the nearest hundredth
Rounding 0.08027 to the nearest hundredth gives: 0.08 cubic feet\boxed{0.08} \, \text{cubic feet}
Understanding the Conversion
Fluid ounces are commonly used for measuring small liquid volumes (like in cooking or beverages), while cubic feet are used for larger volumes (such as in shipping, construction, or storage). Because a cubic foot holds 1,728 cubic inches, and a fluid ounce is less than 2 cubic inches, it takes many fluid ounces to fill even a small fraction of a cubic foot.
In this case, 77 fluid ounces is a little more than half a gallon (1 U.S. gallon = 128 fl oz), which is a relatively small quantity. So, it makes sense that the result in cubic feet is less than 0.1. The final answer, 0.08 cubic feet, reflects this scale difference accurately.
Understanding such conversions is useful in practical fields such as plumbing, shipping, engineering, and environmental science where both U.S. customary and metric systems are used.
