SAT Geometry Word Problems
A cube with edge length of 5 cm is cut into cubes with edge length of 1 cm. If the small cubes along each edge of the big cube are painted, how many small cubes are painted?
(A)
(B)
(C)
(D)
(E)
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Correct Answer: C
Solution:
Tip: Draw a picture.
In order not to count the corner cubes several times, we divide the cubes into corner cubes and edge cubes. The corner cubes are located at the corners, and the edge cubes are those cubes that each edge contributes uniquely.
There are 8 corners, and therefore 8 cubes.
Each edge contributes 5 cubes, 2 of which are corner cubes. Therefore, each edge contributes 5-2=3 unique cubes. A cube has 12 edges. So, we get 3 ⋅ 1 2 = 3 6 edge cubes.
The total number of small cubes that got painted is: #corner cubes + # edge cubes = 8 + 36 = 44.
Incorrect Choices:
If you got this problem wrong, you should review SAT Polygons .
(A)
This is how many corner cubes there are, not how many cubes there are along all of the edges.
(B)
This is how many edge cubes are painted on two of the big cube's faces.
(D)
This is how many cubes are unpainted.
(E)
If you count 12 edges and 5 cubes per edge, you will get this wrong answer. However, each corner cube is lies on 3 edges, and you will have counted it 3 times.