https://file.aiquickdraw.com/mathbot/file/1726494572655qjwhxwaq.jpg

To find the volume of the prism shown in the image, we can split it into two rectangular solids and calculate the volume of each, then sum them up.

### Breakdown of the Prism:
1. **Larger Solid**:
   - Height: \(15 \text{ cm}\)
   - Width: \(5 \text{ cm}\)
   - Depth: \(6 \text{ cm}\)

   Volume of the larger solid:
   \[
   V_1 = 15 \times 5 \times 6 = 450 \text{ cm}^3
   \]

2. **Smaller Solid** (which extends 8 cm from the larger solid):
   - Height: \(15 \text{ cm}\)
   - Width: \(4 \text{ cm}\) (extends beyond the width of the larger solid)
   - Depth: \(1 \text{ cm}\) (6 cm minus the 5 cm width of the larger solid)

   Volume of the smaller solid:
   \[
   V_2 = 15 \times 4 \times 1 = 60 \text{ cm}^3
   \]

### Total Volume:
Combining both parts, the total volume of the prism is:
\[
V_{\text{total}} = V_1 + V_2 = 450 + 60 = 510 \text{ cm}^3
\]

Therefore, the total volume of the prism is \(510 \text{ cm}^3\).

Would you like more details on any step or have any other questions about this solution?

1. How would the volume calculation change if the dimensions of the smaller solid were different?
2. Why do we calculate the volume by splitting the figure into smaller, more manageable parts?
3. What would be the volume if the height of the entire prism was increased or decreased?
4. Could there be any other methods to calculate the volume of such a compound shape?
5. How would the solution change if the prism was standing on one of the smaller faces?

Tip: When calculating the volume of a compound shape, always look for ways to divide the shape into simpler shapes whose volume calculations are straightforward.

The cross-section of the prism below is a compound shape formed of two rectangles. Work out the volume of the prism. Give your answer in cm^3.

Learn how to calculate the volume of a compound shape prism formed of two rectangular solids. The prism has dimensions of 15 cm, 8 cm, 6 cm, 4 cm, and 5 cm, resulting in a total volume of 510 cm^3. This example demonstrates how to split a complex shape into simpler solids to compute the total volume.

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