To find how many 1-inch cubes are needed to fill the bottom layer of the rectangular prism, you can use the area of the base of the prism, which is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
In your case, the length of the prism is 5 inches and the width is 2 inches.
So, the expression to find the number of 1-inch cubes in the bottom layer is:
\[ \text{Number of cubes in each layer} = 5 , \text{inches} \times 2 , \text{inches} = 10 , \text{cubes} \]
If you also want to calculate the total number of layers and the volume of the prism, you would need to know the height of the prism. The volume can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
If you denote the height of the prism as \( h \), then the total number of layers (each 1 inch high) would be:
\[ \text{Number of layers} = h \]
And the total volume of the prism would be:
\[ \text{Volume} = 5 \times 2 \times h = 10h , \text{cubic inches} \]
So to summarize:
- Number of cubes in each layer: \( 5 \times 2 = 10 \)
- Number of layers: \( h \) (where \( h \) is the height of the prism)
- Volume: \( 10h , \text{cubic inches} \)