Let's calculate the volume of each cylindrical container and match them to the appropriate locomotives based on their capacities.
1. Cylinder A:
- Length: 40 ft.
- Diameter: 12 ft.
- Fill level: half
The volume of a cylinder is given by the formula:
[tex]\[
V = \pi \times \left(\frac{d}{2}\right)^2 \times h \times \text{fill level}
\][/tex]
For Cylinder A:
[tex]\[
V_A = \pi \times \left(\frac{12}{2}\right)^2 \times 40 \times \frac{1}{2} = 2261.95 \text{ cubic feet}
\][/tex]
Based on the capacity table:
[tex]\[
2261.95 \text{ cubic feet} \quad (\text{YH61})
\][/tex]
2. Cylinder B:
- Length: 24 ft.
- Diameter: 8 ft.
- Fill level: full
For Cylinder B:
[tex]\[
V_B = \pi \times \left(\frac{8}{2}\right)^2 \times 24 \times 1 = 1206.37 \text{ cubic feet}
\][/tex]
Based on the capacity table:
[tex]\[
1206.37 \text{ cubic feet} \quad (\text{CG35})
\][/tex]
3. Cylinder C:
- Length: 16 ft.
- Diameter: 16 ft.
- Fill level: full
For Cylinder C:
[tex]\[
V_C = \pi \times \left(\frac{16}{2}\right)^2 \times 16 \times 1 = 3216.99 \text{ cubic feet}
\][/tex]
Based on the capacity table:
[tex]\[
3216.99 \text{ cubic feet} \quad (\text{YH61})
\][/tex]
4. Cylinder D:
- Length: 6 ft.
- Diameter: 12 ft.
- Fill level: full
For Cylinder D:
[tex]\[
V_D = \pi \times \left(\frac{12}{2}\right)^2 \times 6 \times 1 = 678.58 \text{ cubic feet}
\][/tex]
Based on the capacity table:
[tex]\[
678.58 \text{ cubic feet} \quad (\text{A450})
\][/tex]
In summary:
- Cylinder A (2261.95 cubic feet) matches with YH61
- Cylinder B (1206.37 cubic feet) matches with CG35
- Cylinder C (3216.99 cubic feet) matches with YH61
- Cylinder D (678.58 cubic feet) matches with A450
The correct pairs are:
- Cylinder A -> YH61
- Cylinder B -> CG35
- Cylinder C -> YH61
- Cylinder D -> A450
