A painted wooden cube whose edge is 3 inches is cut into 27 one-inch cubes. How many of these small cubes have just two painted sides?
a.12
b.18
c.9
d.none of the above
Only the middle piece of the 6 edges have two sides painted, the corners have 3 sides painted
Make yourself a rough sketch to see that.
So there would be 6, but that is not one of the given choices, so, none of the above
umm ... a cube has 12 edges ... and 6 faces
Duhh,
R_scott, you are right, and I even told them to make a sketch.
To find the answer to this question, we need to visualize what happens when the large cube is cut into smaller cubes.
First, let's consider the large cube with an edge of 3 inches. Since each edge is 3 inches long, the volume of the large cube is calculated by cubing the length of the edge:
Volume of large cube = (3 inches) x (3 inches) x (3 inches) = 27 cubic inches
Next, we know that the large cube is cut into 27 one-inch cubes. Each of these smaller cubes will have a volume of 1 cubic inch.
Now, let's examine the cube from different sides. If a small cube is on the inside of the large cube, it will be surrounded by other smaller cubes on all sides and will not have any painted sides.
However, if a small cube is on the surface of the large cube, it will have some of its sides exposed and painted. Let's focus on the small cubes on the surface.
The small cubes on the surface will occupy the following positions:
- The corners of the large cube: There are 8 corners in a cube, and each corner will have exactly 3 sides painted.
- The edges of the large cube (excluding corners): There are 12 edges in a cube, and each edge will have exactly 2 sides painted.
- The faces of the large cube (excluding corners and edges): There are 6 faces in a cube, and each face will have exactly 1 side painted.
To find the total number of small cubes with two painted sides, we need to consider only the small cubes on the edges (excluding corners). Since each edge has 2 small cubes, and there are 12 edges, the total number of small cubes with two painted sides is:
Total number of small cubes with two painted sides = 2 (small cubes per edge) x 12 (number of edges) = 24
Therefore, the correct answer is d. none of the above.
edges of the original cube , but not the corners
looks like a dozen