https://file.aiquickdraw.com/mathbot/file/1729871815478gy7zhn5t.jpg

The image shows the net of a 3D rectangular prism (box) with labeled dimensions.

From the image, here are the key dimensions:
- Short side of the rectangular sections: \(3 \, \text{in.}\)
- Larger rectangular faces: \(7.5 \, \text{in.} \times 11.5 \, \text{in.}\)

This net consists of:
- **Two 7.5 in. by 3 in. rectangles** (top and bottom faces)
- **Two 11.5 in. by 3 in. rectangles** (left and right faces)
- **Two 7.5 in. by 11.5 in. rectangles** (front and back faces)

### Finding the Surface Area
To calculate the total surface area of the prism, we sum the areas of all six rectangles.

1. **Area of two \(7.5 \times 3\) rectangles**:
   \[ 2 \times (7.5 \times 3) = 2 \times 22.5 = 45 \, \text{in}^2 \]

2. **Area of two \(11.5 \times 3\) rectangles**:
   \[ 2 \times (11.5 \times 3) = 2 \times 34.5 = 69 \, \text{in}^2 \]

3. **Area of two \(7.5 \times 11.5\) rectangles**:
   \[ 2 \times (7.5 \times 11.5) = 2 \times 86.25 = 172.5 \, \text{in}^2 \]

### Total Surface Area
\[
45 + 69 + 172.5 = 286.5 \, \text{in}^2
\]

### Volume of the Prism
The volume is calculated using the formula \( V = \text{length} \times \text{width} \times \text{height} \). From the net:
- Length = 11.5 in.
- Width = 7.5 in.
- Height = 3 in.

\[
V = 11.5 \times 7.5 \times 3 = 258.75 \, \text{in}^3
\]

Let me know if this is clear or if you have further questions!

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Here are 5 follow-up questions you might consider:
1. How would the surface area change if the height doubled to 6 inches?
2. What is the lateral surface area of the prism (excluding the top and bottom faces)?
3. How can the volume formula be adapted for irregularly shaped prisms?
4. How does surface area scale compared to volume when the dimensions are doubled?
5. If the box were to be filled with water, how much weight would it hold (assuming 1 cubic inch of water weighs 0.0361 lbs)?

**Tip:** When dealing with nets of 3D shapes, always ensure that all corresponding faces are counted exactly twice to avoid missing any area.

The image shows a net of a rectangular prism with dimensions labeled as follows: 7.5 in. by 3 in. for the top and bottom faces, 11.5 in. by 3 in. for the left and right faces, and 7.5 in. by 11.5 in. for the front and back faces. How do you calculate the surface area and volume?

Learn how to calculate the surface area and volume of a rectangular prism with dimensions 7.5 inches by 3 inches by 11.5 inches. Detailed steps on applying geometric formulas for surface area and volume. Suitable for students in Grades 5-7.

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