Question 58

State whether the following statement is true or false:

A cube of side 3 cm painted on all its faces, when sliced into 1 cubic cm cubes, will have exactly 1 cube with none of its faces painted.

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Solution

True
Given, a cube of side 3 cm is painted on all its faces. Now, it is sliced into 1 cu cm cubes. Then, there will be 8 corner cubes that have 3 sides painted, 6 centre cubes with only one side painted and only 1 cube in the middle that has no side painted.

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Question 1

A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, then how many 1 cubic centimetre cubes will have exactly one of their faces painted?
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A cube of side $5 c m$ is painted on all its faces. If it is sliced into $1$ cubic centimetre cubes, then how many $1$ cubic centimetre cubes will have exactly one of their faces painted?

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