https://file.aiquickdraw.com/mathbot/file/17287019363166xvwqehg.jpg

Let's calculate the volumes of the two compound shapes (a and b) given in the image.

### Shape a
Shape \( a \) is made up of two rectangular prisms:
1. **Bottom section**:
   - Length: \( 15 \, m \)
   - Width: \( 6 \, m \)
   - Height: \( 5 \, m \)
   
   Volume of bottom section:
   \[
   V_1 = 15 \times 6 \times 5 = 450 \, m^3
   \]

2. **Top section**:
   - Length: \( 8 \, m \)
   - Width: \( 6 \, m \)
   - Height: \( 12 - 5 = 7 \, m \)
   
   Volume of top section:
   \[
   V_2 = 8 \times 6 \times 7 = 336 \, m^3
   \]

The total volume of shape \( a \) is:
\[
V_a = V_1 + V_2 = 450 + 336 = 786 \, m^3
\]

### Shape b
Shape \( b \) is also made up of two rectangular prisms:
1. **Top section**:
   - Length: \( 20 \, mm \)
   - Width: \( 7 \, mm \)
   - Depth: \( 9 \, mm \)
   
   Volume of top section:
   \[
   V_3 = 20 \times 7 \times 9 = 1260 \, mm^3
   \]

2. **Bottom section**:
   - Length: \( 6 \, mm \)
   - Width: \( 7 \, mm \)
   - Depth: \( 3 \, mm \)
   
   Volume of bottom section:
   \[
   V_4 = 6 \times 7 \times 3 = 126 \, mm^3
   \]

The total volume of shape \( b \) is:
\[
V_b = V_3 + V_4 = 1260 + 126 = 1386 \, mm^3
\]

### Final Results
- Volume of shape \( a \): \( 786 \, m^3 \)
- Volume of shape \( b \): \( 1386 \, mm^3 \)

Would you like more details or have any questions?

### Related Questions:
1. How would the volumes change if shape \( a \) had a different height for the top section?
2. What is the volume of shape \( b \) in cubic centimeters?
3. How can we calculate the surface area of these compound shapes?
4. If shape \( a \) was scaled down by half, what would be its new volume?
5. What are the differences in calculating volume for other 3D shapes like cylinders or spheres?

### Tip:
Always double-check that all measurements are in the same units when calculating volumes to avoid errors.

Work out the volume of these compound shapes.

Learn how to calculate the volume of compound shapes made of rectangular prisms. This problem breaks down volumes into simple sections, including a detailed step-by-step solution for two shapes. Suitable for Grades 7-9.

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