To determine how many layers of 10 one-inch cubes can fit in the given rectangular prism, we first need to calculate the volume of the rectangular prism and then the volume occupied by the cubes.
Step 1: Calculate the volume of the rectangular prism.
The volume \( V \) of a rectangular prism can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = 5 inches
- Width = 2 inches
- Height = 3 inches
Calculating the volume:
\[ V = 5 \times 2 \times 3 = 30 \text{ cubic inches} \]
Step 2: Calculate the volume occupied by the cubes.
Each 1-inch cube has a volume of 1 cubic inch, and we can fit 10 cubes in one layer. Therefore, the volume of 10 cubes in one layer is:
\[ \text{Volume of 10 cubes} = 10 \text{ cubic inches} \]
Step 3: Calculate the number of layers.
To find how many layers of these cubes can fit in the rectangular prism, divide the total volume of the prism by the volume occupied by one layer of cubes:
\[ \text{Number of layers} = \frac{\text{Volume of prism}}{\text{Volume of one layer of cubes}} = \frac{30 \text{ cubic inches}}{10 \text{ cubic inches}} = 3 \]
Thus, 3 layers of 10 one-inch cubes can fit in the rectangular prism.
Final Answer: 3 layers.