Final answer:
To find how many 1.5 inch cubes fit in a 2.25x3.15x2 inch prism, calculate the volumes of the prism and the cube, then divide the prism's volume by the cube's volume. The result is 4.2, meaning 4 whole cubes can fit.
Step-by-step explanation:
To determine how many cubes with an edge length of 1.5 inches can fit in a rectangular prism measuring 2.25 inches by 3.15 inches by 2 inches, we need to calculate the volume of both the prism and the cube and then divide the prism's volume by the cube's volume.
First, calculate the volume of the rectangular prism:
- Volume of the prism = length × width × height
- Volume of the prism = 2.25 in. × 3.15 in. × 2 in.
- Volume of the prism = 14.175 in.³
Next, calculate the volume of the cube:
- Volume of the cube = side length × side length × side length
- Volume of the cube = 1.5 in. × 1.5 in. × 1.5 in.
- Volume of the cube = 3.375 in.³
To find out how many cubes can fit:
- Cubes that can fit = Volume of the prism / Volume of the cube
- Cubes that can fit = 14.175 in.³ / 3.375 in.³
- Cubes that can fit = 4.2
Since you cannot have a fraction of a cube, the number of whole cubes that can fit inside the prism would be 4.