Measurement, NAPX-G4-NC28 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

722

Question

The edges of a  4×4×4\ 4 × 4×4 cube are formed using blocks as shown below:



In total, 32 blocks are used.

How many blocks would be needed to make the edges of a  6×6×6\ 6 × 6 × 6 cube in the same way?

Worked Solution

Blocks in top layer = 20

Blocks in bottom layer = 20

Other blocks (pillars) = 4 × 4 = 16

∴\therefore Total blocks = 56

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 4 × 4×4$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2016/12/NAP-G4-NC281-259x300.png 200 indent3 vpad
In total, 32 blocks are used. How many blocks would be needed to make the edges of a $\ 6 × 6 × 6$ cube in the same way?
workedSolution
Blocks in top layer = 20 Blocks in bottom layer = 20 Other blocks (pillars) = 4 × 4 = 16 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
56
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer056

Variant 1

DifficultyLevel

720

Question

The edges of a  3×3×3\ 3 × 3 × 3 cube are formed using blocks as shown below:



In total, 20 blocks are used.

How many blocks would be needed to make the edges of a  4×4×4\ 4 × 4 × 4 cube in the same way?

Worked Solution

Blocks in top layer = 12

Blocks in bottom layer = 12

Other blocks (pillars) = 4 × 2 = 8

∴\therefore Total blocks = 32

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 3 × 3 × 3$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-NC28-SA_1.svg 200 indent3 vpad
In total, 20 blocks are used. How many blocks would be needed to make the edges of a $\ 4 × 4 × 4$ cube in the same way?
workedSolution
Blocks in top layer = 12 Blocks in bottom layer = 12 Other blocks (pillars) = 4 × 2 = 8 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
32
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer032

Variant 2

DifficultyLevel

724

Question

The edges of a  5×5×5\ 5 × 5 × 5 cube are formed using blocks as shown below:



In total, 44 blocks are used.

How many blocks would be needed to make the edges of a  7×7×7\ 7 × 7 × 7 cube in the same way?

Worked Solution

Blocks in top layer = 24

Blocks in bottom layer = 24

Other blocks (pillars) = 4 × 5 = 20

∴\therefore Total blocks = 68

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 5 × 5 × 5$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-NC28-SA_2-1.svg 200 indent3 vpad
In total, 44 blocks are used. How many blocks would be needed to make the edges of a $\ 7 × 7 × 7$ cube in the same way?
workedSolution
Blocks in top layer = 24 Blocks in bottom layer = 24 Other blocks (pillars) = 4 × 5 = 20 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
68
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer068

Variant 3

DifficultyLevel

722

Question

The edges of a  6×6×6\ 6 × 6 × 6 cube are formed using blocks as shown below:



In total, 56 blocks are used.

How many blocks would be needed to make the edges of a  8×8×8\ 8 × 8 × 8 cube in the same way?

Worked Solution

Blocks in top layer = 28

Blocks in bottom layer = 28

Other blocks (pillars) = 4 × 6 = 24

∴\therefore Total blocks = 80

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 6 × 6 × 6$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-NC28-SA_3.svg 200 indent3 vpad
In total, 56 blocks are used. How many blocks would be needed to make the edges of a $\ 8 × 8 × 8$ cube in the same way?
workedSolution
Blocks in top layer = 28 Blocks in bottom layer = 28 Other blocks (pillars) = 4 × 6 = 24 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
80
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer080

Variant 4

DifficultyLevel

713

Question

The edges of a  7×7×7\ 7 × 7 × 7 cube are formed using blocks as shown below:



In total, 68 blocks are used.

How many blocks would be needed to make the edges of a  5×5×5\ 5 × 5 × 5 cube in the same way?

Worked Solution

Blocks in top layer = 16

Blocks in bottom layer = 16

Other blocks (pillars) = 4 × 3 = 12

∴\therefore Total blocks = 44

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 7 × 7 × 7$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-NC28-SA_4.svg 200 indent3 vpad
In total, 68 blocks are used. How many blocks would be needed to make the edges of a $\ 5 × 5 × 5$ cube in the same way?
workedSolution
Blocks in top layer = 16 Blocks in bottom layer = 16 Other blocks (pillars) = 4 × 3 = 12 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
44
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer044

Variant 5

DifficultyLevel

725

Question

The edges of a  8×8×8\ 8 × 8 × 8 cube are formed using blocks as shown below:



In total, 80 blocks are used.

How many blocks would be needed to make the edges of a  10×10×10\ 10 × 10 × 10 cube in the same way?

Worked Solution

Blocks in top layer = 36

Blocks in bottom layer = 36

Other blocks (pillars) = 4 × 8 = 32

∴\therefore Total blocks = 104

Question Type

Answer Box

Variables

Variable nameVariable value
question
The edges of a $\ 8 × 8 × 8$ cube are formed using blocks as shown below:
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-NC28-SA_5.svg 200 indent3 vpad
In total, 80 blocks are used. How many blocks would be needed to make the edges of a $\ 10 × 10 × 10$ cube in the same way?
workedSolution
Blocks in top layer = 36 Blocks in bottom layer = 36 Other blocks (pillars) = 4 × 8 = 32 $\therefore$ Total blocks = {{{correctAnswer0}}}
correctAnswer0
104
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0104

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