A 3 cm cube is painted on all its faces.It is then cut into 1 cm cubes. How many cubes will have paint on exactly 2 faces ?
To solve this problem, we need to understand the structure of the 3 cm cube and how it is divided into smaller 1 cm cubes.
First, let's consider the original 3 cm cube. It has 6 faces, and each face is a 3 cm by 3 cm square.
When the cube is cut into 1 cm cubes, it will be divided into smaller cubes along its length, width, and height. Since each edge of the original cube is 3 cm long, it will be divided into 3 smaller cubes along each edge. So, the total number of 1 cm cubes will be 3 x 3 x 3 = 27 cubes.
Now, let's think about how many cubes will have paint on exactly 2 faces. To visualize this, imagine the sides of the original 3 cm cube. Each side will generate a row of 1 cm cubes with paint on exactly 2 faces.
Each side has dimensions of 3 cm x 3 cm, resulting in a square of 9 smaller 1 cm cubes. Since there are 6 sides, there will be a total of 6 x 9 = 54 smaller 1 cm cubes with paint on exactly 2 faces.
So, the answer to the question "How many cubes will have paint on exactly 2 faces?" is 54 cubes.