To calculate the volume of the given shape, which appears to be a triangular prism with a hollow section, follow these steps:

Step 1: Calculate the volume of the entire prism

The volume of a triangular prism is given by: $\text{Volume} = \text{Base Area} \times \text{Length}$

1.1 Calculate the base area of the large triangle

The base of the large triangle is $15 \, \text{cm}$, and the height is $14 \, \text{cm}$. The area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 15 \times 14 = 105 \, \text{cm}^2$

1.2 Multiply by the length of the prism

The length of the prism is $6 \, \text{cm}$: $\text{Volume of large prism} = 105 \times 6 = 630 \, \text{cm}^3$

Step 2: Calculate the volume of the hollow section

The hollow section is another triangular prism inside the larger prism.

2.1 Calculate the base area of the smaller triangle

The base of the smaller triangle is $4 \, \text{cm}$, and the height is $3 \, \text{cm}$. Using the same formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 4 \times 3 = 6 \, \text{cm}^2$

2.2 Multiply by the length of the prism

The length of the smaller prism is also $6 \, \text{cm}$: $\text{Volume of smaller prism} = 6 \times 6 = 36 \, \text{cm}^3$

Step 3: Subtract the hollow section volume from the total volume

$\text{Total Volume} = \text{Volume of large prism} - \text{Volume of smaller prism}$ $\text{Total Volume} = 630 - 36 = 594 \, \text{cm}^3$

Final Answer:

The volume of the shape is: $\boxed{594 \, \text{cm}^3}$

Would you like a detailed explanation of any step or additional clarification?

Here are 5 related questions to deepen your understanding:

1. How is the formula for the volume of a triangular prism derived?
2. How would the answer change if the hollow section's length was different from the outer prism's length?
3. Can you calculate the surface area of this shape?
4. What would happen if the shape had multiple hollow sections?
5. How can this problem be applied to real-world situations, such as calculating the volume of a water tank?

Tip: Always double-check the dimensions and units in problems like this to avoid errors in your calculations.