The Math practice question for the day is a Mensuration (Solid Geometry) question. This question is based on testing concepts of cubes.

Question
A cube of side 5cm 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?

A. 9
B. 61
C. 98
D. 54
E. 64

The correct choice is (D) and the correct answer is 54.

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.

This eBook with over 200 pages covers basic to advanced concepts in Geometry starting with lines, triangles to other polygons and circles. Each of these concepts is explained with illustrative examples wherever applicable.

The book contains over 50+ solved examples and illustrative examples. In addition, the eBook contains 60+ exercise questions covering a wide variety of questions from these three topics for you to practise.
Read More.. | eBook FAQ | Download Now!