Find the total surface area of one of small cubes to that of the larger cube if a cube of edge 5cm is cut into cubes, each of edge 1cm.
the linear scale is 1:5
so, the areas are in the ratio 1:25
To find the total surface area of one of the small cubes, we need to know the surface area of one face of the small cube.
The surface area of a cube is given by the formula: Surface Area = 6 * (side length)^2.
For the larger cube with an edge length of 5cm, the surface area is:
Surface Area of the larger cube = 6 * (5cm)^2 = 6 * 25cm^2 = 150cm^2.
To find the surface area of one of the small cubes, we need to first determine the number of small cubes that can be cut from the larger cube. Since each side of the small cube has an edge length of 1cm, we can use the formula:
Number of small cubes = (side length of larger cube / side length of small cube)^3.
Number of small cubes = (5cm / 1cm)^3 = 5^3 = 125.
Therefore, 125 small cubes can be cut from the larger cube.
Now, to find the surface area of one small cube, we divide the total surface area of the larger cube by the number of small cubes:
Surface Area of one small cube = Surface Area of larger cube / Number of small cubes
Surface Area of one small cube = 150cm^2 / 125 = 1.2cm^2.
So, the total surface area of one small cube is 1.2cm^2.
To summarize, the total surface area of one of the small cubes is 1.2cm^2, and this is 1/125th (or 0.8%) of the surface area of the larger cube.