A solid cube of side 12 cm is cut into 8 Identical
cubes. What will be the side of the new cube?
Also, find the ratio between the surface area
of the original cube and the total surface area
nf all the small cubes formed.
Answers
Answer:
When a cube of side length "a" is divided into smaller cubes, each of the smaller cubes will have side length "a/n", where n is the number of smaller cubes that the original cube was divided into. In this case, the original cube has a side length of 12 cm and it was divided into 8 smaller cubes. Therefore, the side length of each of the smaller cubes will be 12 cm / 8 = 1.5 cm.
The surface area of the original cube is 6 times the area of one face, so it is equal to 6a^2. The total surface area of all the smaller cubes can be found by multiplying the surface area of one smaller cube by the number of smaller cubes. The surface area of one smaller cube is 6 times the area of one face, which is (a/n)^2. Therefore, the total surface area of all the smaller cubes is 6 * n * (a/n)^2 = 6n(a^2)/n^2 = 6a^2 / n.
The ratio between the surface area of the original cube and the total surface area of all the smaller cubes is 6a^2 / (6a^2 / n) = n. In this case, the original cube has a side length of 12 cm and was divided into 8 smaller cubes, so the ratio is 8. This means that the total surface area of all the smaller cubes is equal to 1/8 of the surface area of the original cube