To calculate the weight of the barley in the railroad container, we first need to determine the volume of the container and then find out how much of that volume is filled with barley.
Step 1: Convert the dimensions of the container to feet.
The dimensions of the container are:
- Length: 51'6" = 51 + 6/12 = 51.5 feet
- Width: 7'0" = 7 feet
- Height: 7'6" = 7 + 6/12 = 7.5 feet
Step 2: Calculate the total volume of the container.
Volume = Length × Width × Height
Volume = 51.5 ft × 7 ft × 7.5 ft
Calculating this:
\[ Volume = 51.5 \times 7 \times 7.5 = 51.5 \times 52.5 = 2703.75 \text{ cubic feet} \]
Step 3: Since the container is ¾ full, calculate the filled volume.
Volume of barley = \(\frac{3}{4} \times 2703.75\)
\[ Volume_{barley} = 0.75 \times 2703.75 = 2027.8125 \text{ cubic feet} \]
Step 4: Calculate the weight of the barley using the density.
Density of barley = 37 pounds per cubic foot.
Weight = Volume × Density
Weight = \(2027.8125 \text{ cubic feet} \times 37 \text{ pounds/cubic foot}\)
Calculating this:
\[ Weight = 2027.8125 \times 37 = 75000.0625 \text{ pounds} \]
Step 5: Round to the nearest whole pound.
Weight ≈ 75,000 pounds.
Looking at the options provided, it seems that there isn't an exact match for 75,000, but the closest option is:
A. 75,029 pounds
Therefore, the answer is:
A. 75,029 pounds
1 answer