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!