Answer:
Therefore, 991 of the original 1 cm cubes are NOT used to make the larger cube.
Explanation:
To solve this problem, we need to find the number of 1 cm cubes that are used to make the larger cube and subtract it from the total number of 1 cm cubes obtained when the solid 10 cm cube is cut into smaller cubes.
The total number of 1 cm cubes obtained from cutting the solid 10 cm cube is calculated by finding the volume of the larger cube divided by the volume of the smaller cube.
Volume of the larger cube = (10 cm)^3 = 1000 cm^3
Volume of the smaller cube = (1 cm)^3 = 1 cm^3
Number of 1 cm cubes obtained = Volume of the larger cube / Volume of the smaller cube = 1000 cm^3 / 1 cm^3 = 1000 cubes
Now, let's find the number of 1 cm cubes used to make the larger cube. Since the larger cube is hollow inside, we need to calculate the volume of the hollow space.
The side length of the larger cube can be found by taking the cube root of the volume of the solid 10 cm cube. So, side length = cube root of (10 cm^3) = 10^(1/3) cm.
The volume of the hollow space can be calculated by subtracting the volume of the smaller cube from the volume of the larger cube.
Volume of the hollow space = Volume of the larger cube - Volume of the smaller cube = (side length)^3 - (1 cm)^3 = (10^(1/3) cm)^3 - 1 cm^3
Now, let's calculate the number of 1 cm cubes used to make the larger cube.
Number of 1 cm cubes used = Volume of the hollow space / Volume of the smaller cube = [(10^(1/3) cm)^3 - 1 cm^3] / 1 cm^3
Simplifying further, we have:
Number of 1 cm cubes used = (10^(1/3))^3 - 1 = 10 - 1 = 9 cubes
Finally, to find the number of 1 cm cubes that are NOT used to make the larger cube, we subtract the number of cubes used from the total number of 1 cm cubes obtained:
Number of cubes NOT used = Total number of 1 cm cubes - Number of 1 cm cubes used = 1000 cubes - 9 cubes = 991 cubes
Therefore, 991 of the original 1 cm cubes are NOT used to make the larger cube.