Measurement, NAPX-I4-CA30 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

740

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 78 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 78
12×8.8×12×w\dfrac{1}{2} \times 8.8 \times 12 \times \large w = 78
w\large w = 7852.8\dfrac{78}{52.8}
= 1.477... cm

∴\therefore Maximum triangular prisms that fit
= 401.477...\dfrac{40}{1.477...}
= 27.07...
= 27 triangular prisms

Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA30.svg 370 indent vpad Each smaller triangular prism is 78 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-I4-CA301.svg 260 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 78| |$\dfrac{1}{2} \times 8.8 \times 12 \times \large w$|= 78| |$\large w$|= $\dfrac{78}{52.8}$| ||= 1.477... cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{40}{1.477...}$| |= 27.07...| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
27
prefix0
suffix0
triangular prisms

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
correctAnswer027

triangular prisms

Variant 1

DifficultyLevel

738

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 95 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit into the larger one.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 95
12×9.8×15×w\dfrac{1}{2} \times 9.8 \times 15 \times \large w = 95
w\large w = 9573.5\dfrac{95}{73.5}
= 1.292... cm

∴\therefore Maximum triangular prisms that fit
= 601.2925...\dfrac{60}{1.2925...}
= 46.42...
= 46 triangular prisms



Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_0_a.svg 500 indent vpad Each smaller triangular prism is 95 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_0_b.svg 320 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit into the larger one. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 95| |$\dfrac{1}{2} \times 9.8 \times 15 \times \large w$|= 95| |$\large w$|= $\dfrac{95}{73.5}$| ||= 1.292... cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{60}{1.2925...}$| |= 46.42...| |= {{{correctAnswer0}}} {{{suffix0}}}|

correctAnswer0
46
prefix0
suffix0
triangular prisms

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
correctAnswer046

triangular prisms

Variant 2

DifficultyLevel

736

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 80 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit into the larger one.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 80
12×6.2×8×w\dfrac{1}{2} \times 6.2 \times 8 \times \large w = 80
w\large w = 8024.8\dfrac{80}{24.8}
= 3.225... cm

∴\therefore Maximum triangular prisms that fit
= 603.2258...\dfrac{60}{3.2258...}
= 18.6
= 18 triangular prisms



Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_2_a-2.svg 480 indent vpad Each smaller triangular prism is 80 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_2_b.svg 300 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit into the larger one. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 80| |$\dfrac{1}{2} \times 6.2 \times 8 \times \large w$|= 80| |$\large w$|= $\dfrac{80}{24.8}$| ||= 3.225... cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{60}{3.2258...}$| |= 18.6| |= {{{correctAnswer0}}} {{{suffix0}}}|

correctAnswer0
18
prefix0
suffix0
triangular prisms

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
correctAnswer018

triangular prisms

Variant 3

DifficultyLevel

734

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 200 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit into the larger one.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 200
12×18×11×w\dfrac{1}{2} \times 18 \times 11 \times \large w = 200
w\large w = 20099\dfrac{200}{99}
= 2.02... cm

∴\therefore Maximum triangular prisms that fit
= 1002.02...\dfrac{100}{2.02...}
= 49.5...
= 49 triangular prisms



Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_3_c.svg 480 indent vpad Each smaller triangular prism is 200 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_3_b.svg 300 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit into the larger one. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 200| |$\dfrac{1}{2} \times 18 \times 11 \times \large w$|= 200| |$\large w$|= $\dfrac{200}{99}$| ||= 2.02... cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{100}{2.02...}$| |= 49.5...| |= {{{correctAnswer0}}} {{{suffix0}}}|

correctAnswer0
49
prefix0
suffix0
triangular prisms

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
correctAnswer049

triangular prisms

Variant 4

DifficultyLevel

732

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 330 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit into the larger one.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 330
12×10.8×12×w\dfrac{1}{2} \times 10.8 \times 12 \times \large w = 330
w\large w = 33064.8\dfrac{330}{64.8}
= 5.09... cm

∴\therefore Maximum triangular prisms that fit
= 505.09...\dfrac{50}{5.09...}
= 9.8181...
= 9 triangular prisms

Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_4_c.svg 480 indent vpad Each smaller triangular prism is 330 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_4_b.svg 300 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit into the larger one. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 330| |$\dfrac{1}{2} \times 10.8 \times 12 \times \large w$|= 330| |$\large w$|= $\dfrac{330}{64.8}$| ||= 5.09... cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{50}{5.09...}$| |= 9.8181...| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
9
prefix0
suffix0
triangular prisms

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
correctAnswer09

triangular prisms

Variant 5

DifficultyLevel

730

Question

A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below.

Each smaller triangular prism is 660 cm³ in size.

What is the maximum number of smaller triangular prisms that can fit inside the box?

Worked Solution

The dimensions of the smaller triangular prism fit into the larger one.

Find the smaller triangular prism's width (w\large w):
A×wA \times \large w = 660
12×15×20×w\dfrac{1}{2} \times 15 \times 20 \times \large w = 660
w\large w = 660150\dfrac{660}{150}
= 4.4 cm

∴\therefore Maximum triangular prisms that fit
= 804.4\dfrac{80}{4.4}
= 18.1818...
= 18 triangular prisms

Question Type

Answer Box

Variables

Variable nameVariable value
question
A box in the shape of a triangular prism is used to store smaller triangular prism pieces as shown below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_5_a.svg 480 indent vpad Each smaller triangular prism is 660 cm³ in size. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-–-NAPX-I4-CA30-SA_5_b.svg 300 indent vpad What is the maximum number of smaller triangular prisms that can fit inside the box?
workedSolution
The dimensions of the smaller triangular prism fit into the larger one. Find the smaller triangular prism's width ($\large w$):
||| |-:|-| |$A \times \large w$|= 660| |$\dfrac{1}{2} \times 15 \times 20 \times \large w$|= 660| |$\large w$|= $\dfrac{660}{150}$| ||= 4.4 cm|

sm_nogap $\therefore$ Maximum triangular prisms that fit
>>|| |-| |= $\dfrac{80}{4.4}$| |= 18.1818...| |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
18
prefix0
suffix0
triangular prisms

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
correctAnswer018

triangular prisms

Tags

  • ms_ca