To solve this problem, let's calculate the volume of the octagonal prism-shaped tank, as the cost of filling the tank depends on its volume.

Given Information

1. The tank has an octagonal prism shape.
2. Each side of the octagon (base) measures $1.4 \, \text{m}$.
3. The height of the tank is $5 \, \text{m}$.
4. The area of each octagonal surface (base) is $9 \, \text{m}^2$.
5. The cost of filling the container with water is $2 \, \text{USD per} \, \text{m}^3$.

Solution Steps

1. Calculate the Volume of the Tank:

   • Since it is an octagonal prism, the volume $V$ can be calculated by: $V = \text{Area of Base} \times \text{Height}$
   • Using the given area of the base as $9 \, \text{m}^2$ and height as $5 \, \text{m}$: $V = 9 \, \text{m}^2 \times 5 \, \text{m} = 45 \, \text{m}^3$

2. Calculate the Cost to Fill the Tank:

   • The cost per cubic meter of water is $2 \, \text{USD}$.
   • Therefore, the total cost $C$ to fill the tank is: $C = V \times \text{Cost per cubic meter} = 45 \, \text{m}^3 \times 2 \, \text{USD/m}^3 = 90 \, \text{USD}$

Answer

The cost to fill the container is $90.

Would you like more details on this calculation, or do you have any questions?

Here are five related questions you might find useful:

1. How is the area of an octagon calculated if not provided?
2. What if the cost per cubic meter of water changed; how would that affect the calculation?
3. How does the shape of the base affect the volume calculation for different prisms?
4. What if the tank had a slanted height; how would the calculation change?
5. Can we apply a similar volume calculation for irregular-shaped containers?

Tip: For prism-shaped containers, the volume is always the area of the base multiplied by the height, regardless of the shape of the base.