Crude oil is being transferred from a full rectangular storage container with dimensions of 4 meters by 9 meters by 10 meters into cylinders transportation contanier that has a diameter of 6 meters. What is the minimum possible length for transportation container that will hold all of the oil?

Options

A. `40pi`
B. `(40)/(pi)`
C. `60pi`
D. `(120)/(pi)`

Answer

To find the minimum possible length of the cylindrical transportation container that will hold all of the crude oil, we can follow these steps:

### Step 1: Calculate the volume of the rectangular storage container.
The volume \( V \) of a rectangular prism is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
For the given dimensions of the rectangular container (4 meters by 9 meters by 10 meters):
\[ V = 4 \, \text{m} \times 9 \, \text{m} \times 10 \, \text{m} = 360 \, \text{m}^3 \]

### Step 2: Determine the radius of the cylindrical container.
The diameter of the cylindrical container is given as 6 meters. The radius \( r \) is half of the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{6 \, \text{m}}{2} = 3 \, \text{m} \]

### Step 3: Write the volume formula for the cylindrical container.
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( h \) is the height (or length) of the cylinder. Substituting the radius:
\[ V = \pi (3 \, \text{m})^2 h = 9\pi h \]

### Step 4: Set the volume of the rectangular container equal to the volume of the cylindrical container.
Since the volume of oil remains the same during the transfer, we can set the two volumes equal to each other:
\[ 360 \, \text{m}^3 = 9\pi h \]

### Step 5: Solve for \( h \).
To find \( h \), rearrange the equation:
\[ h = \frac{360}{9\pi} \]
Simplifying this gives:
\[ h = \frac{40}{\pi} \, \text{m} \]

### Conclusion:
The minimum possible length for the cylindrical transportation container that will hold all of the oil is:
\[ \boxed{\frac{40}{\pi} \, \text{m}} \]