A cube with length 4cm is divided into 8 identical cubes.How much greater is the combined surface area of the 8 smaller cubes than the surface area of the original cube?
8 cubes of side 2 have surface
8(6*2^2)
one cube of side 4 has surface
6*4^2
To find the combined surface area of the 8 smaller cubes, we first need to determine the surface area of one smaller cube.
Since a cube has six identical square faces, the surface area of the original cube is calculated by multiplying the length of one side by itself and then multiplying the result by 6.
Surface area of original cube = 6 * (side length)^2
= 6 * (4cm)^2
= 6 * 16cm^2
= 96cm^2
Now that we know the surface area of the original cube, we can calculate the surface area of one smaller cube. Since the original cube is divided into 8 identical smaller cubes, each smaller cube will have a side length of 4cm/2 = 2cm.
Surface area of one smaller cube = 6 * (side length)^2
= 6 * (2cm)^2
= 6 * 4cm^2
= 24cm^2
To find the combined surface area of the 8 smaller cubes, we multiply the surface area of one smaller cube by the number of smaller cubes.
Combined surface area of the 8 smaller cubes = 24cm^2 * 8
= 192cm^2
To find the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube, we subtract the surface area of the original cube from the combined surface area of the smaller cubes.
Difference = Combined surface area of the 8 smaller cubes - Surface area of original cube
= 192cm^2 - 96cm^2
= 96cm^2
Therefore, the combined surface area of the 8 smaller cubes is 96cm^2 greater than the surface area of the original cube.