Measurement, NAPX-F4-CA31 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

723

Question

Three identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 1029 cubic centimetres, what it its height?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
3a\large a3^3 = 1029
a\large a3^3 = 343
a\large a = 3433\sqrt[3]{343}
= 7 cm

∴h\therefore \large h = 3 × 7
= 21 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA31-SA.svg 170 indent3 vpad
If the prism has a volume of 1029 cubic centimetres, what it its height?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |3$\large a$$^3$|= 1029| |$\large a$$^3$|= 343| |$\large a$|= $\sqrt[3]{343}$| ||= 7 cm|

||| |-|-| |$\therefore \large h$|= 3 × 7 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
21
prefix0
suffix0
cm

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
correctAnswer021

cm

Variant 1

DifficultyLevel

726

Question

Three identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 5184 cubic centimetres, what it its height?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
3a\large a3^3 = 5184
a\large a3^3 = 1728
a\large a = 17283\sqrt[3]{1728}
= 12 cm

∴h\therefore \large h = 3 × 12
= 36 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-F4-CA31-SA_1.svg 170 indent3 vpad
If the prism has a volume of 5184 cubic centimetres, what it its height?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |3$\large a$$^3$|= 5184| |$\large a$$^3$|= 1728| |$\large a$|= $\sqrt[3]{1728}$| ||= 12 cm|

||| |-|-| |$\therefore \large h$|= 3 × 12 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
36
prefix0
suffix0
cm

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
correctAnswer036

cm

Variant 2

DifficultyLevel

724

Question

Four identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 500 cubic centimetres, what it its height?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
4a\large a3^3 = 500
a\large a3^3 = 125
a\large a = 1253\sqrt[3]{125}
= 5 cm

∴h\therefore \large h = 4 × 5
= 20 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Four identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX-F4-CA31-SA_v2.svg 170 indent3 vpad
If the prism has a volume of 500 cubic centimetres, what it its height?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |4$\large a$$^3$|= 500| |$\large a$$^3$|= 125| |$\large a$|= $\sqrt[3]{125}$| ||= 5 cm|

||| |-|-| |$\therefore \large h$|= 4 × 5 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
20
prefix0
suffix0
cm

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
correctAnswer020

cm

Variant 3

DifficultyLevel

725

Question

Four identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 2048 cubic centimetres, what it its height?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
4a\large a3^3 = 2048
a\large a3^3 = 512
a\large a = 5123\sqrt[3]{512}
= 8 cm

∴h\therefore \large h = 4 × 8
= 32 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Four identical cubes are placed on top of each other to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX-F4-CA31-SA_v3.svg 170 indent3 vpad
If the prism has a volume of 2048 cubic centimetres, what it its height?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |4$\large a$$^3$|= 2048| |$\large a$$^3$|= 512| |$\large a$|= $\sqrt[3]{512}$| ||= 8 cm|

||| |-|-| |$\therefore \large h$|= 4 × 8 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
32
prefix0
suffix0
cm

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

cm

Variant 4

DifficultyLevel

724

Question

Five identical cubes are placed side by side to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 6655 cubic centimetres, what it its length?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
5a\large a3^3 = 6655
a\large a3^3 = 1331
a\large a = 13313\sqrt[3]{1331}
= 11 cm

∴l\therefore \large l = 5 × 11
= 55 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Five identical cubes are placed side by side to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX-F4-CA31-SA_v4.svg 400 indent3 vpad
If the prism has a volume of 6655 cubic centimetres, what it its length?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |5$\large a$$^3$|= 6655| |$\large a$$^3$|= 1331| |$\large a$|= $\sqrt[3]{1331}$| ||= 11 cm|

||| |-|-| |$\therefore \large l$|= 5 × 11 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
55
prefix0
suffix0
cm

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
correctAnswer055

cm

Variant 5

DifficultyLevel

725

Question

Six identical cubes are placed side by side to form a rectangular prism as shown in the diagram below.



If the prism has a volume of 4374 cubic centimetres, what it its length?

Worked Solution

Let dimensions of one cube = a\large a × a\large a × a\large a
6a\large a3^3 = 4374
a\large a3^3 = 729
a\large a = 7293\sqrt[3]{729}
= 9 cm

∴l\therefore \large l = 6 × 9
= 54 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
Six identical cubes are placed side by side to form a rectangular prism as shown in the diagram below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX-F4-CA31-SA_v5.svg 400 indent3 vpad
If the prism has a volume of 4374 cubic centimetres, what it its length?
workedSolution
sm_nogap Let dimensions of one cube = $\large a$ × $\large a$ × $\large a$
||| |-:|-| |6$\large a$$^3$|= 4374| |$\large a$$^3$|= 729| |$\large a$|= $\sqrt[3]{729}$| ||= 9 cm|

||| |-|-| |$\therefore \large l$|= 6 × 9 | | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
54
prefix0
suffix0
cm

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
correctAnswer054

cm

Tags

  • ms_ca