Measurement, NAPX-G4-CA31 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

738

Question

Lux is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Lux keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Give your answer to 2 decimal places.

Worked Solution

Area of trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 0.7 × (0.4 + 0.76)
= 0.406 m2^2

Volume = AhA\large h
= 0.406 × 0.8
= 0.3248
= 0.32 m3^3 (to 2 d.p.)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Lux is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/05/NAPX-G4-CA31-SA.svg 350 indent vpad
Lux keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres? Give your answer to 2 decimal places.
workedSolution
sm_nogap Area of trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 0.7 × (0.4 + 0.76)| |= 0.406 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.406 × 0.8| ||= 0.3248| ||= {{{correctAnswer0}}} {{{suffix0}}} (to 2 d.p.)|
correctAnswer0
0.32
prefix0
suffix0
m$^3$

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
correctAnswer00.32

m3^3

Variant 1

DifficultyLevel

740

Question

Manny is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Manny keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Give your answer to 2 decimal places.

Worked Solution

Area of trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 1.5 × (0.6 + 0.72)
= 0.99 m2^2

Volume = AhA\large h
= 0.99 × 0.5
= 0.495
= 0.50 m3^3 (to 2 d.p.)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Manny is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA31-SA_1.svg 500 indent vpad
Manny keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres? Give your answer to 2 decimal places.
workedSolution
sm_nogap Area of trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 1.5 × (0.6 + 0.72)| |= 0.99 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.99 × 0.5| ||= 0.495| ||= {{{correctAnswer0}}} {{{suffix0}}} (to 2 d.p.)|
correctAnswer0
0.50
prefix0
suffix0
m$^3$

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
correctAnswer00.50

m3^3

Variant 2

DifficultyLevel

739

Question

Bree is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Bree keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Give your answer to 2 decimal places.

Worked Solution

Area of trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 0.4 × (0.12 + 0.17)
= 0.058 m2^2

Volume = AhA\large h
= 0.058 × 0.5
= 0.029
= 0.03 m3^3 (to 2 d.p.)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bree is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA31-SA_2.svg 550 indent vpad
Bree keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres? Give your answer to 2 decimal places.
workedSolution
sm_nogap Area of trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 0.4 × (0.12 + 0.17)| |= 0.058 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.058 × 0.5| ||= 0.029| ||= {{{correctAnswer0}}} {{{suffix0}}} (to 2 d.p.)|
correctAnswer0
0.03
prefix0
suffix0
m$^3$

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
correctAnswer00.03

m3^3

Variant 3

DifficultyLevel

737

Question

Carrie is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Carrie keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Give your answer to 2 decimal places.

Worked Solution

Area of trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 0.35 × (0.175 + 0.19)
= 0.063875 m2^2

Volume = AhA\large h
= 0.063875 × 0.4
= 0.02555
= 0.03 m3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Carrie is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA31-SA_3.svg 550 indent vpad
Carrie keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres? Give your answer to 2 decimal places.
workedSolution
sm_nogap Area of trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 0.35 × (0.175 + 0.19)| |= 0.063875 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.063875 × 0.4| ||= 0.02555| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
0.03
prefix0
suffix0
m$^3$

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
correctAnswer00.03

m3^3

Variant 4

DifficultyLevel

739

Question

Blaze is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Blaze keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Give your answer to 2 decimal places.

Worked Solution

Area of larger trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 0.5 × (0.15 + 0.5)
= 0.1625 m2^2

Volume = AhA\large h
= 0.1625 × 0.55
=0.089375
= 0.09 m3^3 (to 2 d.p.)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Blaze is a carpenter. He cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA31-SA_4.svg 500 indent vpad
Blaze keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres? Give your answer to 2 decimal places.
workedSolution
sm_nogap Area of **larger** trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 0.5 × (0.15 + 0.5)| |= 0.1625 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.1625 × 0.55| ||=0.089375| ||= {{{correctAnswer0}}} {{{suffix0}}} (to 2 d.p.)|
correctAnswer0
0.09
prefix0
suffix0
m$^3$

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
correctAnswer00.09

m3^3

Variant 5

DifficultyLevel

742

Question

Olive is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.



Olive keeps the larger piece of wood which is in the shape of a trapezoidal prism.

What is the volume of the larger piece of wood in cubic metres?

Worked Solution

Area of larger trapezoid (face)
= 12h\dfrac{1}{2}\large h(a\large a + b)\large b)
= 12\dfrac{1}{2} × 0.8 × (0.6 + 1.4)
= 0.8 m2^2

Volume = AhA\large h
= 0.8 × 0.5
= 0.40 m3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Olive is a carpenter. She cuts a block of wood in the shape of a rectangular prism along the cut line shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA31-SA_5.svg 550 indent vpad
Olive keeps the larger piece of wood which is in the shape of a trapezoidal prism. What is the volume of the larger piece of wood in cubic metres?
workedSolution
sm_nogap Area of **larger** trapezoid (face)
>>|| |-| |= $\dfrac{1}{2}\large h$($\large a$ + $\large b)$| |= $\dfrac{1}{2}$ × 0.8 × (0.6 + 1.4)| |= 0.8 m$^2$|

||| |-|-| |Volume |= $A\large h$| ||= 0.8 × 0.5| ||= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
0.40
prefix0
suffix0
m$^3$

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
correctAnswer00.40

m3^3

Tags