Question: Dan carved this solid out of wood. Find the volume of the solid.
The solid is an irregular stepped rectangular prism with dimensions labeled $8$ in along the bottom front edge, $6$ in along the left side height, $4$ in for the upper right vertical segment, $7$ in for the middle width/depth segment, $7$ in for the right middle vertical segment, and $4$ in for the lower right vertical segment. position_hint=center
$V$ in$^3$
1. **State the problem:** We need to find the volume of an irregular stepped rectangular prism with given dimensions.
2. **Understand the shape:** The solid can be divided into two rectangular prisms stacked vertically:
- Bottom prism with dimensions: length $8$ in, width $7$ in, height $4$ in (lower right vertical segment).
- Top prism with dimensions: length $8$ in, width $7$ in, height $6 - 4 = 2$ in (difference between left side height and lower right vertical segment).
3. **Formula for volume of a rectangular prism:**
$$V = \text{length} \times \text{width} \times \text{height}$$
4. **Calculate volume of bottom prism:**
$$V_1 = 8 \times 7 \times 4 = 224$$
5. **Calculate volume of top prism:**
$$V_2 = 8 \times 7 \times 2 = 112$$
6. **Calculate total volume:**
$$V = V_1 + V_2 = 224 + 112 = 336$$
7. **Answer:** The volume of the solid is $336$ cubic inches.