Concept explainers
a.
Complete the table.
a.
Answer to Problem 107E
Explanation of Solution
Given information:
A
Complete the table to determine how many unit cubes of the
Calculation:
The unit cube at centre does not have any face blue.
Hence, the numbers of unit cubes with no blue face is
The middle unit cube on each face has only one blue face.
There are
Hence, the numbers of unit cube with only one blue face are,
There are
Rest of the ccubes has three blue faces.
Hence, total numbers of cubes having three blue faces are,
Hence, the table is as follows,
Hence, the table completed.
b.
Complete the table for the other cubes.
b.
Answer to Problem 107E
Explanation of Solution
Given information:
Repeat part (a) for a
Calculation:
The unit cube at centre does not have any face blue.
Hence, the numbers of unit cubes with no blue face is
The middle unit cube on each face has only one blue face.
There are
Hence, the numbers of unit cube with only one blue face are,
There are
Rest of the ccubes has three blue faces.
Hence, total numbers of cubes having three blue faces are,
For the other cubes the table is as follows,
Hence, the table completed.
c.
Observe the pattern.
c.
Answer to Problem 107E
Explanation of Solution
Given information:
What type of pattern do you observe?
Calculation:
Following pattern is observed,
Number of cubes with no blue faces:
This is simplified as the following sequence,
Therefore, the
Numbers of cube with one blue faces:
This is simplified as the following sequence,
Hence, the
Numbers of cube with two blue faces:
This is simplified as the following sequence,
Hence, the
d.
Complete the table for an
d.
Answer to Problem 107E
Explanation of Solution
Given information:
Write formulas you could use to repeat part (a) for an
Calculation:
The unit cube at centre does not have any face blue.
Hence, the numbers of unit cubes with no blue face is
The middle unit cube on each face has only one blue face.
There are
Hence, the numbers of unit cube with only one blue face are,
There are
Rest of the ccubes has three blue faces.
Hence, total numbers of cubes having three blue faces are,
Writing all these in a table we get,
Chapter 9 Solutions
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