1. **State the problem:** Stephanie puts 30 cubes in a box. Each cube is $\frac{1}{2}$ inch on each side. The box holds 2 layers with 15 cubes in each layer. We need to find the volume of the box. 2. **Understand the dimensions:** Each cube has side length $\frac{1}{2}$ inch. 3. **Calculate the volume of one cube:** $$\text{Volume of one cube} = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \text{ cubic inches}$$ 4. **Calculate the total volume of 30 cubes:** $$30 \times \frac{1}{8} = \frac{30}{8} = \frac{15}{4} = 3\frac{3}{4} \text{ cubic inches}$$ 5. **Check the box dimensions given:** The box dimensions are 2 1/2 inches (length), 1 1/2 inches (width), and 1 inch (height). 6. **Calculate the volume of the box using dimensions:** $$2\frac{1}{2} \times 1\frac{1}{2} \times 1 = \frac{5}{2} \times \frac{3}{2} \times 1 = \frac{15}{4} = 3\frac{3}{4} \text{ cubic inches}$$ 7. **Conclusion:** The volume of the box is $3\frac{3}{4}$ cubic inches. This matches the total volume of the 30 cubes, confirming the calculation.