The problem in the image states:

Problem: Stephanie puts 30 cubes in a box. The cubes are $\frac{1}{2}$ inch on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?

Step-by-step solution:

1. Volume of one cube: The side length of each cube is $\frac{1}{2}$ inch. The volume $V$ of a cube is given by the formula: $V = \text{side}^3 = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \text{ cubic inches}$ So, the volume of each cube is $\frac{1}{8}$ cubic inches.

2. Total number of cubes: The box contains 30 cubes, with 15 cubes in each of 2 layers.

3. Volume of the box: The volume of the box is simply the combined volume of all the cubes, as the cubes completely fill the box. $\text{Total volume} = 30 \times \frac{1}{8} = \frac{30}{8} = 3.75 \text{ cubic inches}$

Thus, the correct answer for the volume of the box is 3.75 cubic inches, which corresponds to the option $3 \frac{3}{4}$ cubic inches.

Do you have any questions or would you like more details?

Here are 5 related questions to explore:

1. How do you calculate the volume of different shapes, such as spheres or cylinders?
2. How would the volume change if the side length of each cube doubled?
3. Can you find the surface area of the entire box given the side lengths of the cubes?
4. What is the formula for the volume of a rectangular prism, and how does it apply here?
5. How would the volume change if the box had 3 layers instead of 2?

Tip: Always check if units are consistent (e.g., inches or centimeters) when calculating volumes in word problems.