To find the volume of this irregular prism, we can divide it into two rectangular prisms, calculate the volume of each, and then add them together.

Step-by-Step Solution:

1. Identify Dimensions of Each Prism:

   • Bottom Prism:
     • Length = $3 \, \text{cm}$
     • Width = $3 \, \text{cm}$
     • Height = $2 \, \text{cm}$
   • Top Prism:
     • Length = $1 \, \text{cm}$
     • Width = $3 \, \text{cm}$
     • Height = $5 \, \text{cm}$

2. Calculate the Volume of Each Prism:

   • Volume of Bottom Prism:
     $V_{\text{bottom}} = 3 \times 3 \times 2 = 18 \, \text{cm}^3$
   • Volume of Top Prism:
     $V_{\text{top}} = 1 \times 3 \times 5 = 15 \, \text{cm}^3$

3. Add the Volumes: $V_{\text{total}} = V_{\text{bottom}} + V_{\text{top}} = 18 + 15 = 33 \, \text{cm}^3$

Answer:

The volume of the prism is 33 cubic centimeters.

Would you like further details or have any questions?

1. What is the general formula for the volume of a rectangular prism?
2. How can we calculate the volume of irregular 3D shapes by dividing them into simpler shapes?
3. What are other methods to find the volume of composite shapes?
4. Why is it important to ensure all angles are right angles in this problem?
5. How would the approach change if any of the angles were not 90 degrees?

Tip: When finding volumes of composite shapes, always ensure all parts are calculated separately before summing them up.