Mensuration : Cubes - CAT 2010 Preparation
Question 4 the day:
May 22, 2006
The question for the day is a sample practice problem in Mensuration, a Geometry Topic. The problem provides an understanding of the concept of surface area of a cube, the sides of a cube and concept associated with the faces of a painted cube being sliced into smaller cubes.
Question:
A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
- 9
- 61
- 98
- 54
Correct Answer - 54. Choice (4)
Explanatory Answer
When a 5 cc cube is sliced into 1 cc cubes, we will get 5*5*5 = 125 1 cc cubes.
In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.
Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.
In each face of the larger cube, there will be 5*5 = 25 cubes. Of these, there will be 16 cubes on the edge and 3*3 = 9 cubes which are not on the edge.
Therefore, there will be 9 1-cc cubes per face that will have exactly one of their sides painted.
In total, there will be 9*6 = 54 such cubes.
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