Let's break down the problem step by step: ## 1. **Understand the Shape** The garden bed is L-shaped. To find its volume, **divide the L-shape into two rectangles** and calculate the volume of each, then add them together. ## 2. **Label the Parts** Let's call: - The **long section**: 6 ft by 2 ft by 6 ft - The **short section**: 4 ft by 2 ft by 4 ft But notice: The overlap (where the rectangles intersect) must only be counted once! ### Let's clarify by drawing the dimensions: - The long rectangle is 6 ft (length) × 2 ft (width) × 6 ft (height). - The short rectangle is 4 ft (length) × 2 ft (width) × 4 ft (height). But both rectangles share a **2 ft by 2 ft by 2 ft** cube at the corner. We need to **subtract this overlap**. --- ## 3. **Calculate Each Volume** ### **Long Rectangle:** \[ \text{Volume}_1 = \text{length} \times \text{width} \times \text{height} = 6 \times 2 \times 2 = 24 \text{ ft}^3 \] ### **Short Rectangle:** \[ \text{Volume}_2 = 4 \times 2 \times 2 = 16 \text{ ft}^3 \] ### **Overlap (corner):** \[ \text{Overlap Volume} = 2 \times 2 \times 2 = 8 \text{ ft}^3 \] --- ## 4. **Total Volume** \[ \text{Total Volume} = \text{Volume}_1 + \text{Volume}_2 - \text{Overlap Volume} \] \[ \text{Total Volume} = 24 + 16 - 8 = 32 \text{ ft}^3 \] --- ## **Final Answer** **Mollie needs 32 cubic feet of soil to fill her raised L-shaped garden bed.**