Calculating the Number of Cubes

To determine the number of cubes that can be made from a meter cube with a surface area of 24 sq. dm, we need to follow a step-by-step process. Let's break it down:

Step 1: Determine the Volume of a Cube
- The surface area of a cube is given as 24 sq. dm.
- To calculate the volume of a cube, we need to find the side length (s) of the cube.
- The formula for the surface area of a cube is: SA = 6s^2, where SA is the surface area and s is the side length.
- Rearranging the formula, we have s^2 = SA/6.
- Substituting the surface area value of 24 sq. dm, we get s^2 = 24/6 = 4.
- Taking the square root of both sides, we find s = 2 dm.

Step 2: Determine the Volume of a Meter Cube
- A meter cube has a volume of 1 cubic meter (1 m^3).
- Since 1 meter is equal to 10 decimeters (1 m = 10 dm), the volume can also be expressed as 10 dm x 10 dm x 10 dm = 1000 cubic decimeters (1000 dm^3).

Step 3: Calculate the Number of Cubes
- Now that we know the side length of each cube (2 dm) and the volume of the meter cube (1000 dm^3), we can calculate the number of cubes.
- The volume of each cube is given by V = s^3, where V is the volume and s is the side length.
- Substituting the side length value of 2 dm, we have V = 2^3 = 8 cubic decimeters per cube.
- To find the number of cubes that can be made, we divide the total volume of the meter cube by the volume of each cube: 1000 dm^3 / 8 dm^3 = 125 cubes.

Conclusion
Therefore, from a meter cube with a surface area of 24 sq. dm, we can make 125 cubes, each with a surface area of 24 sq. dm.