A cube painted blue on all faces is cut into 1331 cubes of equal size. How many cubes are painted on one face only?.
Question
A cube painted blue on all faces is cut into 1331 cubes of equal size. How many cubes are painted on one face only?.
Solution
To solve this problem, we first need to understand the structure of the cube.
-
A cube has 6 faces, and if it's painted on all faces, then when it's cut into smaller cubes, the smaller cubes will have paint on them depending on their location.
-
The cubes that are inside the big cube will have no paint on them. The cubes that are on the edges will have paint on 1, 2, or 3 faces.
-
The number of smaller cubes can be found by taking the cube root of 1331, which is 11. This means the big cube was cut into 11 cubes along each edge.
-
The cubes with paint on only one face are the ones that are not on an edge. This means they are not on the top or bottom face (2 faces) and not on the four sides (4 faces).
-
So, the cubes with one face painted are the ones on the four sides, not counting the ones on the top and bottom.
-
Each side has (11-2) * (11-2) = 9 * 9 = 81 cubes with one face painted.
-
Since there are 4 sides, the total number of cubes with one face painted is 4 * 81 = 324.
So, there are 324 smaller cubes that are painted on one face only.
Similar Questions
The following question is based on the information given below:1. All the faces of a big cube are painted with blue colour.2. The cube is cut into 64 small and equal size cubes.How many small cubes are there whose atleast two faces are coloured?(1) 28 (2) 32 (3) 24 (4) 3
A cube is painted on all sides and then cut into 'N' smaller cubes. What is the value of 'N' if there are exactly 8 smaller cubes painted on exactly 3 faces?a.27b.124c.Cannot be determinedd.64
pair of opposite faces of a cube is painted yellow another pair of opposite faces orange and the remaining faces white. The cube is then cut in to 343 smaller but identical cubes.How many of the smaller cubes have exactly one colour on them? a.144 b.150 c.125 d.130
125 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces2.How many of the smaller cubes have exactly one face painted?
A cube is painted red on two adjacent surfaces and black on the surfaces opposite to red surfaces and green on the remaining faces. Now the cube is cut into sixty four smaller cubes of equal sizeHow many smaller cubes have less than three surface painted?48242856
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.