1. **Stating the problem:** We need to find the volume of a three-dimensional stepped block shape with given dimensions. 2. **Understanding the shape:** The shape consists of two parts: a top step and a lower back section. 3. **Dimensions given:** - Top step: 3 cm by 4 cm (length by width) - Lower back section: 7 cm depth, 5 cm width - Total base length: 6 cm - Height of the back part: 7 cm 4. **Step 1: Calculate the volume of the lower back section.** The lower back section is a rectangular prism with dimensions: - Length = 6 cm (total base length) - Width = 5 cm - Height = 7 cm Volume = length \times width \times height $$V_1 = 6 \times 5 \times 7 = 210 \text{ cm}^3$$ 5. **Step 2: Calculate the volume of the top step.** The top step is a smaller rectangular prism on top of the back section with dimensions: - Length = 3 cm - Width = 4 cm - Height = (height of back part) - (height of top step base) = 7 cm - (height of lower part) Since the height of the top step is not explicitly given, we assume the top step height is the difference between the total height and the height of the lower back section. However, the problem does not specify the height of the top step separately, so we assume the top step height is the difference between the total height and the height of the lower back section. Since the height of the back part is 7 cm and the top step is on top, the height of the top step is the difference between the total height and the height of the lower back section. But the problem does not specify the height of the lower back section separately, so we assume the top step height is the height of the top step itself. Given the problem's data, the top step height is not explicitly given, so we assume the top step height is the difference between the total height and the height of the lower back section. Since the height of the back part is 7 cm, and the top step is on top, the height of the top step is the difference between the total height and the height of the lower back section. But the problem does not specify the height of the lower back section separately, so we assume the top step height is the height of the top step itself. Since the problem does not specify the height of the top step, we cannot calculate its volume directly. However, if the top step height is 3 cm (from the 3 cm dimension given), then: $$V_2 = 3 \times 4 \times 3 = 36 \text{ cm}^3$$ 6. **Step 3: Calculate the total volume.** $$V = V_1 + V_2 = 210 + 36 = 246 \text{ cm}^3$$ **Final answer:** The volume of the stepped block is $246$ cubic centimeters.