
Concept explainers
(a)
To find:
The number of cubes painted on 4 sides.

Answer to Problem 1CR
Solution:
0 cubes.
Explanation of Solution
Calculation:
Given a 4-cm cube painted green is cut into 64 1-cm cubes.
There will be no cube with all 4 sides painted on.
Final statement:
0 cubes will be painted on 4 sides.
(b)
To find:
The number of cubes painted on 3 sides.

Answer to Problem 1CR
Solution:
8 cubes.
Explanation of Solution
Calculation:
From the picture, the cubes painted on 3 sides are the cubes in the corner of the 4-cm cube.
The number of corners is 8.
Hence there are 8 cubes painted on 3 sides.
Final statement:
8 cubes will be painted on 3 sides.
(c)
To find:
The number of cubes painted on 2 sides.

Answer to Problem 1CR
Solution:
24 cubes.
Explanation of Solution
Calculation:
From the picture, the cubes painted on 2 sides are the cubes in the middle of the sides of the 4-cm cube.
There are 2 cubes in each side of the 4-cm cube.
The number of sides is 12.
The number of cubes is
Hence there are 24 cubes painted on 2 sides.
Final statement:
24 cubes will be painted on 2 sides.
(d)
To find:
The number of cubes painted on 1 side.

Answer to Problem 1CR
Solution:
24 cubes.
Explanation of Solution
Calculation:
From the picture, the cubes painted on 1 side are the cubes in the middle of the faces of the 4-cm cube.
There are 4 cubes in each face of the 4-cm cube.
The number of faces is 6.
The number of cubes is
Hence there are 24 cubes painted on 1 side.
Final statement:
24 cubes will be painted on 1 side.
(e)
To find:
The number of cubes painted on 0 sides.

Answer to Problem 1CR
Solution:
8 cubes.
Explanation of Solution
Calculation:
Total number of cubes is 64.
The number of cubes painted on 4 sides is 0.
The number of cubes painted on 3 sides is 8.
The number of cubes painted on 2 sides is 24.
The number of cubes painted on 1 side is 24.
Total number of painted cubes
The number of cubes painted on 0 sides is
Final statement:
8 cubes will be painted on 0 sides.
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Chapter 7 Solutions
Nature of Mathematics (MindTap Course List)
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- 2arrow_forwardAn engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. 2 Miles x = 1 Mile R 10 miles miles y = milesarrow_forwardhelp on this, results givenarrow_forward
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