A cube of side 3 cm painted on all its faces, when sliced into 1 cubic centimetre cubes, will have exactly 1 cube with none of its faces painted. Is the given statement true or false
Solution:
The diagram below shows a cube of side 3 cm which is sliced into 27 cubes of 1 cm side.
We will have 8 corner cubes that have 3 sides painted, 6 centre cubes(in the middle row, middle column) with only one side painted and only 1 cube in the middle of the entire cube that has no side painted.
The centre column as shown above has three cubes, one of which does not have any face painted. In fact it is located right in the centre of the cube.
Therefore there is only One 1 cm Cube in the centre of the 3 cm cube which has no face painted.
The statement is therefore True(T).
✦ Try This: A cube of side 4 cm painted on all its faces, when sliced into 1 cubic centimetre cubes, will have exactly 8 cubes with none of its faces painted. Is the given statement true or false
A cube of 4 cm is shown below broken into 64 1 cm cubes.
From the diagram above it is evident that the eight cubes in the centre of the 4 cm cube do not have any of the faces painted.
Hence the statement is true
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 58
A cube of side 3 cm painted on all its faces, when sliced into 1 cubic centimetre cubes, will have exactly 1 cube with none of its faces painted. Is the given statement true or false
Summary:
A cube of side 3 cm painted on all its faces, when sliced into 1 cubic centimetre cubes, will have exactly 1 cube with none of its faces painted. The statement is true
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