https://file.aiquickdraw.com/mathbot/file/1725000072746acrtmsir.jpg

To find the volume of the shape shown in the image, we can consider it as a three-dimensional object with a hollow rectangular prism cut out from a larger rectangular prism.

**Step 1: Determine the dimensions of the outer and inner rectangular prisms.**

1. **Outer prism dimensions:**
   - Length: 11 cm
   - Width: 8 cm
   - Height (thickness): 4.5 cm

2. **Inner prism dimensions (hollow part):**
   - Length: 7 cm
   - Width: (Since the width is not given directly, we'll assume it to be the same as the length for simplicity, which is 7 cm).
   - Height (thickness): 7.25 cm (This height is larger than the outer height, indicating the inner prism is a vertical cut that goes beyond the outer height).

**Step 2: Calculate the volume of the outer rectangular prism.**

\[
\text{Volume of outer prism} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
= 11 \, \text{cm} \times 8 \, \text{cm} \times 4.5 \, \text{cm}
\]

\[
= 396 \, \text{cm}^3
\]

**Step 3: Calculate the volume of the inner rectangular prism (hollow part).**

\[
\text{Volume of inner prism} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
= 7 \, \text{cm} \times 7 \, \text{cm} \times 7.25 \, \text{cm}
\]

\[
= 356.75 \, \text{cm}^3
\]

**Step 4: Calculate the volume of the solid part by subtracting the volume of the inner prism from the volume of the outer prism.**

\[
\text{Volume of solid part} = \text{Volume of outer prism} - \text{Volume of inner prism}
\]
\[
= 396 \, \text{cm}^3 - 356.75 \, \text{cm}^3
\]

\[
= 39.25 \, \text{cm}^3
\]

**Final Answer:**
The volume of the solid part of the shape is \( 39.25 \, \text{cm}^3 \).

---

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. How would the volume change if the thickness of the outer prism increased?
2. What would the volume be if the inner prism had a different height?
3. How do we calculate the surface area of the remaining solid part?
4. How does the position of the hollow part affect the overall volume?
5. What is the effect of changing only one dimension of either the inner or outer prism on the volume?

**Tip:** When dealing with composite shapes, always calculate the volume of each part separately before combining them.

Learn how to calculate the volume of a hollow rectangular prism with detailed steps and formulas. This problem involves finding the volume of a solid shape with a cut-out inner prism, including dimensions and calculations. Suitable for Grades 6-8.

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