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Drag the tiles to the boxes to form correct pairs.

At a railway yard, locomotives are used to haul containers carrying oil. A locomotive is chosen according to the volume of oil it can haul, as shown in the table.
\begin{tabular}{|l|l|}
\hline Locomotive & Capacity \\
\hline A450 & [tex]$0-750$[/tex] cubic feet \\
\hline CG35 & [tex]$750-1,500$[/tex] cubic feet \\
\hline BR73 & [tex]$1,500-2,500$[/tex] cubic feet \\
\hline YH61 & [tex]$2,500-3,500$[/tex] cubic feet \\
\hline
\end{tabular}

The four cylindrical containers listed in the table need to be hauled.
\begin{tabular}{|l|c|c|l|}
\hline Cylinder & Length (ft.) & Diameter (ft.) & Fill Level \\
\hline A & 40 & 12 & half \\
\hline B & 24 & 8 & full \\
\hline C & 16 & 16 & full \\
\hline D & 6 & 12 & full \\
\hline
\end{tabular}

Match each container to the locomotive needed to haul it.

A. A450
B. CG35
C. BR73
D. YH61

1. Cylinder A
2. Cylinder B
3. Cylinder C
4. Cylinder D



Answer :

GinnyAnswer
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

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