Measurement, NAPX-J4-CA39 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

770

Question

A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, in cubic centimetres?

Worked Solution

Volume of rectangular prism
= 42 × 48 × 82
= 165 312 cm3^3

∴\therefore Volume of 1 triangular prism
= 165 312 ÷ 6
= 27 552 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-J4-CA39.svg 320 indent3 vpad
What is the volume of one triangular prism, in cubic centimetres?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 42 × 48 × 82| |= 165 312 cm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 165 312 ÷ 6| |= 27 552 {{{suffix0}}}|
correctAnswer0
27552
prefix0
suffix0
cm$^3$

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
correctAnswer027552

cm3^3

Variant 1

DifficultyLevel

770

Question

A rectangular prism is made by stacking 8 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, in cubic centimetres?

Worked Solution

Volume of rectangular prism
= 18 × 24 × 44
= 19 008 cm3^3

∴\therefore Volume of 1 triangular prism
= 19 008 ÷ 8
= 2376 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 8 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-J4-CA39-SA_1.svg 400 indent vpad
What is the volume of one triangular prism, in cubic centimetres?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 18 × 24 × 44| |= 19 008 cm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 19 008 ÷ 8| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
2376
prefix0
suffix0
cm$^3$

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
correctAnswer02376

cm3^3

Variant 2

DifficultyLevel

775

Question

A rectangular prism is made by stacking 12 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, in cubic centimetres?

Worked Solution

Volume of rectangular prism
= 84 × 62 × 123
= 640 584 cm3^3

∴\therefore Volume of 1 triangular prism
= 640 584 ÷ 12
= 53 382 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 12 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement^J-NAPX-J4-CA39-SA_2.svg 400 indent vpad
What is the volume of one triangular prism, in cubic centimetres?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 84 × 62 × 123| |= 640 584 cm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 640 584 ÷ 12| |= 53 382 {{{suffix0}}}|
correctAnswer0
53382
prefix0
suffix0
cm$^3$

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
correctAnswer053382

cm3^3

Variant 3

DifficultyLevel

773

Question

A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, in cubic centimetres?

Worked Solution

Volume of rectangular prism
= 264 × 125 × 85
= 2 805 000 cm3^3

∴\therefore Volume of 1 triangular prism
= 2 805 000 ÷ 6
= 467 500 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 6 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement^J-NAPX-J4-CA39-SA_3.svg 450 indent vpad
What is the volume of one triangular prism, in cubic centimetres?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 264 × 125 × 85| |= 2 805 000 cm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 2 805 000 ÷ 6| |= 467 500 {{{suffix0}}}|
correctAnswer0
467500
prefix0
suffix0
cm$^3$

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
correctAnswer0467500

cm3^3

Variant 4

DifficultyLevel

772

Question

A rectangular prism is made by stacking 8 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, in cubic centimetres?

Worked Solution

Volume of rectangular prism
= 80 × 35 × 64
= 179 200 cm3^3

∴\therefore Volume of 1 triangular prism
= 179 200 ÷ 8
= 22 400 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 8 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement^J-NAPX-J4-CA39-SA_4.svg 440 indent3 vpad
What is the volume of one triangular prism, in cubic centimetres?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 80 × 35 × 64| |= 179 200 cm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 179 200 ÷ 8| |= 22 400 {{{suffix0}}}|
correctAnswer0
22400
prefix0
suffix0
cm$^3$

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
correctAnswer022400

cm3^3

Variant 5

DifficultyLevel

779

Question

A rectangular prism is made by stacking 10 identical triangular prisms, as pictured below.



What is the volume of one triangular prism, to the nearest cubic millimetre?

Worked Solution

Volume of rectangular prism
= 118 × 102 × 188
= 2 262 768 mm3^3

∴\therefore Volume of 1 triangular prism
= 2 262 768 ÷ 10
= 226 277 mm3^3  (nearest mm3^3)

Question Type

Answer Box

Variables

Variable nameVariable value
question
A rectangular prism is made by stacking 10 identical triangular prisms, as pictured below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement^J-NAPX-J4-CA39-SA_5.svg 370 indent3 vpad
What is the volume of one triangular prism, to the nearest **cubic millimetre**?
workedSolution
sm_nogap Volume of rectangular prism
>>|| |-| |= 118 × 102 × 188| |= 2 262 768 mm$^3$|

sm_nogap $\therefore$ Volume of 1 triangular prism
>>|| |-| |= 2 262 768 ÷ 10| |= 226 277 {{{suffix0}}}|
correctAnswer0
226277
prefix0
suffix0
mm$^3$  (nearest mm$^3$)

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
correctAnswer0226277

mm3^3  (nearest mm3^3)

Tags

  • ms_ca