Number 4. A cube is decorated by gluing identical gray squares onto it. All the faces of the cube look the same. How many gray squares are there in total? Feel free to pause and try and solve it. Okay, so first let's just start trying to count the number of gray squares we see. And to figure this out, let's look at it one face at a time, right? Because every single face, as we see in the problem, every single face looks the same. So we can start and see, well, there's one square in the middle, one gray square in the middle of each of these faces, right? And remember, a cube, this is important to know, has six faces. So there's going to be six of these gray squares, one on each of the middle faces, right? But then we also have these other ones on the edges, right? And we can see that there's four on each of these faces, but they sort of go over the edge. And in fact, the trick is to notice that there's one, exactly one on each edge, right? This edge has this square over here. For example, this edge has this square over here. This edge has this square over here, right? So the number of these gray squares is just going to be how many edges there are. So another important thing to know, there are always 12 edges on a cube. In fact, that's true for any rectangular prism. But there's going to be six faces and one on each of these faces, and then 12 edges and then one on each of those edges. And we can see that there's no other squares. All of them are either in the middle of a face or they're on one of the edges. So that's everything. So if we add that up, 6 plus 12 is 18, which is option B. So the answer to number 4 is B.

cube

gray squares

geometry

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edges