Convert 0.092 ft3 to L. (2.54 cm = 1 in., 1 L = 1 dm3)
[A] 2.6 L
[B] 3.2 × 10-3 L
[C]0.40 L
[D]1.8 L
[E]26 L
The Correct Answer and Explanation is :
To convert 0.092 cubic feet (ft³) to liters (L), let’s break the process into steps.
Step 1: Convert cubic feet to cubic inches
Since we know that 1 foot = 12 inches, we can convert cubic feet to cubic inches using the conversion factor:
[
1 \, \text{ft} = 12 \, \text{in.}
]
This means:
[
1 \, \text{ft}^3 = 12^3 \, \text{in.}^3 = 1728 \, \text{in.}^3
]
Therefore, to convert 0.092 ft³ to cubic inches:
[
0.092 \, \text{ft}^3 \times 1728 \, \text{in.}^3/\text{ft}^3 = 158.4 \, \text{in.}^3
]
Step 2: Convert cubic inches to cubic centimeters
We are given the conversion factor 2.54 cm = 1 inch, which implies:
[
1 \, \text{in.} = 2.54 \, \text{cm}
]
So, to convert cubic inches to cubic centimeters (cm³), we cube the linear conversion factor:
[
1 \, \text{in.}^3 = (2.54)^3 \, \text{cm}^3 = 16.387 \, \text{cm}^3
]
Now, we convert 158.4 in³ to cm³:
[
158.4 \, \text{in.}^3 \times 16.387 \, \text{cm}^3/\text{in.}^3 = 2597.4 \, \text{cm}^3
]
Step 3: Convert cubic centimeters to liters
We are also given that 1 liter (L) = 1 cubic decimeter (dm³) and that:
[
1 \, \text{dm} = 10 \, \text{cm}
]
Therefore, 1 dm³ = 1000 cm³. Now, we convert 2597.4 cm³ to liters:
[
2597.4 \, \text{cm}^3 \div 1000 = 2.6 \, \text{L}
]
Thus, the correct answer is [A] 2.6 L.
Explanation Summary:
- We first converted cubic feet to cubic inches (0.092 ft³ to 158.4 in³).
- Then, we converted cubic inches to cubic centimeters using the conversion factor (158.4 in³ to 2597.4 cm³).
- Finally, we converted cubic centimeters to liters (2597.4 cm³ to 2.6 L).
This approach is based on standard unit conversions between length, volume, and mass.
I’ll generate an image to illustrate this conversion process.
Here is the educational illustration that visually demonstrates the conversion process from 0.092 cubic feet to liters. It breaks down the steps clearly, showing how to convert cubic feet to cubic inches, cubic inches to cubic centimeters, and cubic centimeters to liters.
Let me know if you need any further clarification!
