To find the volume of this shape, we need to break it down into two smaller rectangular prisms and then calculate the volumes separately.

Step 1: Identify the two sections

1. Larger rectangular prism: This prism has the following dimensions:

   • Length = 7 cm
   • Width = 6 cm
   • Height = 1 cm

   Volume of larger section = Length × Width × Height
   $= 7 \, \text{cm} \times 6 \, \text{cm} \times 1 \, \text{cm} = 42 \, \text{cm}^3$

2. Smaller cut-out rectangular prism: This cut-out is subtracted from the larger prism and has:

   • Length = 3 cm
   • Width = 2 cm
   • Height = 1 cm

   Volume of smaller cut-out section = Length × Width × Height
   $= 3 \, \text{cm} \times 2 \, \text{cm} \times 1 \, \text{cm} = 6 \, \text{cm}^3$

Step 2: Subtract the smaller cut-out volume from the larger volume

$\text{Total Volume} = 42 \, \text{cm}^3 - 6 \, \text{cm}^3 = 36 \, \text{cm}^3$

Final Answer:

The volume of the given shape is 36 cm³.

Would you like further details or clarifications? Here are some related questions:

1. How can you break down other complex 3D shapes to find their volume?
2. What if the height of the shape changed? How would the volume calculation be affected?
3. How do you handle volumes when shapes have slanted or angled faces?
4. What is the difference between calculating volume and surface area?
5. How would you find the volume if this were a hollow shape?

Tip: When finding the volume of irregular shapes, break them down into smaller known shapes (like cubes or rectangular prisms) for easier calculation.