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The shape of the sculpture is a combination of a rectangular prism and a half-cylinder.

### Step 1: Volume of the Rectangular Prism
The dimensions of the rectangular prism are:
- Length: 8.3 cm
- Width: 3.1 cm
- Height: 3.4 cm (which is the same as the radius of the half-cylinder).

The volume \( V_{\text{prism}} \) of the rectangular prism is calculated as:
\[
V_{\text{prism}} = \text{length} \times \text{width} \times \text{height}
\]
\[
V_{\text{prism}} = 8.3 \, \text{cm} \times 3.1 \, \text{cm} \times 3.4 \, \text{cm}
\]

### Step 2: Volume of the Half-Cylinder
The half-cylinder has:
- Radius \( r = 3.4 \, \text{cm} \)
- Length \( l = 8.3 \, \text{cm} \)

The volume \( V_{\text{half-cylinder}} \) of the half-cylinder is calculated as:
\[
V_{\text{half-cylinder}} = \frac{1}{2} \times \pi r^2 l
\]
\[
V_{\text{half-cylinder}} = \frac{1}{2} \times \pi \times (3.4 \, \text{cm})^2 \times 8.3 \, \text{cm}
\]

### Step 3: Total Volume
The total volume \( V_{\text{total}} \) of the sculpture is the sum of the rectangular prism and the half-cylinder:
\[
V_{\text{total}} = V_{\text{prism}} + V_{\text{half-cylinder}}
\]

Now, I will calculate the values.The total volume of the sculpture is \( 238.2 \, \text{cm}^3 \), rounded to one decimal place.

Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How is the volume of a cylinder calculated?
2. What is the difference between the volume of a full cylinder and a half-cylinder?
3. How do different shapes affect volume calculations?
4. Why is the volume of the prism calculated as length × width × height?
5. How would the volume change if the radius of the half-cylinder were smaller?

**Tip**: When solving composite volume problems, break down the object into simpler shapes and sum their volumes!

A sculptor takes a large piece of clay, and after flattening some sides and curving others ends up with the shape below. The dimensions are: length = 8.3 cm, width = 3.1 cm, and height/radius = 3.4 cm. Find the volume of the resulting sculpture.

Learn how to calculate the volume of a composite shape made up of a rectangular prism and a half-cylinder. The dimensions are length = 8.3 cm, width = 3.1 cm, and height/radius = 3.4 cm. This problem involves basic geometry and volume calculation, suitable for Grades 8-10.

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