To calculate the total volume of the shape, we will combine the volumes of the cuboid and the pyramid.

1. Volume of the cuboid:

The cuboid has dimensions:

• Length = $20 \, \text{cm}$,
• Width = $20 \, \text{cm}$,
• Height = $32 \, \text{cm}$.

The volume of a cuboid is calculated as: $V_{\text{cuboid}} = \text{length} \times \text{width} \times \text{height}$ $V_{\text{cuboid}} = 20 \times 20 \times 32 = 12,800 \, \text{cm}^3$

2. Volume of the pyramid:

The pyramid has:

• Base area (same as the top face of the cuboid) = $20 \, \text{cm} \times 20 \, \text{cm} = 400 \, \text{cm}^2$,
• Height = $15 \, \text{cm}$.

The volume of a pyramid is given by: $V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}$ $V_{\text{pyramid}} = \frac{1}{3} \times 400 \times 15 = \frac{1}{3} \times 6,000 = 2,000 \, \text{cm}^3$

3. Total volume:

The total volume is: $V_{\text{total}} = V_{\text{cuboid}} + V_{\text{pyramid}}$ $V_{\text{total}} = 12,800 + 2,000 = 14,800 \, \text{cm}^3$

Final Answer:

The volume of the shape is: $\boxed{14,800 \, \text{cm}^3}$

Would you like further clarification or breakdown of any steps?

Related Questions:

1. How is the volume of other 3D shapes calculated?
2. What happens to the volume if the dimensions of the pyramid are doubled?
3. How do the height and base area of a pyramid affect its volume?
4. What is the relationship between the cuboid and pyramid in this shape?
5. Can this composite shape be classified as a specific type of 3D figure?

Tip: Always ensure the base dimensions of a pyramid align with the dimensions of the shape it is attached to.