The number of cubes that fit into the prism is not equivalent to Mai's approach of multiplying the edge lengths and then by 27. The correct method involves dividing the prism's volume by the cube's volume.
The prism has dimensions of 5 units by 5 units by 8 units. The volume of the prism (V_prism) is found by multiplying its length, width, and height:
Volume of the prism = 5 units * 5 units * 8 units
Now, cubes with an edge length of 1 unit can fit into the prism. The volume of one cube (V_cube) is given by the formula "edge length cubed," which in this case is 1 unit cubed.
The number of cubes that can fit into the prism is the ratio of the prism's volume to the cube's volume:
Number of cubes = V_prism / V_cube
Substitute the values:
Number of cubes = (5 units * 5 units * 8 units) / (1 unit cubed)
Now, consider Mai's statement. She suggests multiplying the edge lengths of the prism and then multiplying the result by 27:
Mai's approach = 5 units * 5 units * 8 units * 27
Now, let's compare the two results:
Number of cubes: 5 * 5 * 8 = 200 cubes
Mai's approach: 5 * 5 * 8 * 27 = 5400
These results are not equal, so it seems that Mai's statement is not correct. The correct approach is to find the number of cubes by dividing the volume of the prism by the volume of one cube.
Complete question:
Cubes with edge length of unit fit in a prism that is 5 units by 5 units by 8 units. Mai says that we can also find the answer by multiplying the edge lengths of the prism and then multiplying the result by 27. Do you agree with her statement? Explain your reasoning.