Measurement, NAPX-G4-CA22 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

685

Question

Jerry cut a golf ball into two halves.


The following calculation gives the approximate volume of one half of the ball in cm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Radius = 2 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 23\times\ 2^3
= 16.74...
≈\approx 17 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Jerry cut a golf ball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/07/NAPX-G4-CA22-SA_1.svg 200 indent3 vpad The following calculation gives the approximate volume of one half of the ball in cm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
sm_nogap Radius = 2 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 2^3$| ||= 16.74...| ||$\approx$ {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
17
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
correctAnswer017

cm3^3

Variant 1

DifficultyLevel

685

Question

Patty cut a basketball into two halves.


The following calculation gives the approximate volume of one half of the ball in cm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Radius = 12 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 123\times\ 12^3
= 3617.28
≈\approx 3617 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Patty cut a basketball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA22-SA_basketball_v1.svg 190 indent3 vpad The following calculation gives the approximate volume of one half of the ball in cm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
sm_nogap Radius = 12 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 12^3$| ||= 3617.28| ||$\approx$ {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
3617
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
correctAnswer03617

cm3^3

Variant 2

DifficultyLevel

687

Question

Ricky cut a cricket ball into two halves.


The following calculation gives the approximate volume of one half of the ball in mm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Using 1 cm = 10 mm

Radius = 3.6 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 3.63\times\ 3.6^3
= 97.66...
≈\approx 98 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ricky cut a cricket ball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA22-SA_cricketball_1.svg 200 indent3 vpad The following calculation gives the approximate volume of one half of the ball in mm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
Using 1 cm = 10 mm sm_nogap Radius = 3.6 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 3.6^3$| ||= 97.66...| ||$\approx$ {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
98
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
correctAnswer098

cm3^3

Variant 3

DifficultyLevel

685

Question

Becky imagined cutting a beach ball into two halves.


The following calculation gives the approximate volume of one half of the ball in cm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Radius = 25 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 253\times\ 25^3
= 32 708.33...32\ 708.33...
≈\approx 32 70832\ 708 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Becky imagined cutting a beach ball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA22-SA_beachball_1a.svg 170 indent3 vpad The following calculation gives the approximate volume of one half of the ball in cm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
sm_nogap Radius = 25 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 25^3$| ||= $32\ 708.33...$| ||$\approx$ $32\ 708$ cm$^3$|
correctAnswer0
32708
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
correctAnswer032708

cm3^3

Variant 4

DifficultyLevel

685

Question

Diego cut a soccer ball into two halves.


The following calculation gives the approximate volume of one half of the ball in cm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Radius = 11 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 113\times\ 11^3
= 2786.22...
≈\approx 2786 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Diego cut a soccer ball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA22-SA_soccerball_1.svg 170 indent3 vpad The following calculation gives the approximate volume of one half of the ball in cm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
sm_nogap Radius = 11 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 11^3$| ||= 2786.22...| ||$\approx$ {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
2786
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
correctAnswer02786

cm3^3

Variant 5

DifficultyLevel

685

Question

Cher cut a mirror ball into two halves.


The following calculation gives the approximate volume of one half of the ball in cm3^3.

Volume = 12×43π\dfrac{1}{2} \times \dfrac{4}{3} \large \pi × r\times\ \large r3,^3, where π\large \pi = 3.14


What volume does the calculation give, to the nearest cm³, where r\large r is the radius of the ball?

Worked Solution

Radius = 40 cm
∴V\therefore V = 12×43×π\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi × 403\times\ 40^3
= 133 973.33...
= 133 973 cm3^3

Question Type

Answer Box

Variables

Variable nameVariable value
question
Cher cut a mirror ball into two halves.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-G4-CA22-SA_mirrorball_1.svg 170 indent3 vpad The following calculation gives the approximate volume of one half of the ball in cm$^3$. >>Volume = $\dfrac{1}{2} \times \dfrac{4}{3} \large \pi$ $\times\ \large r$$^3,$ where $\large \pi$ = 3.14
What volume does the calculation give, to the nearest cm³, where $\large r$ is the radius of the ball?
workedSolution
sm_nogap Radius = 40 cm
||| |-|-| |$\therefore V$| = $\dfrac{1}{2} \times \dfrac{4}{3} \times \large \pi$ $\times\ 40^3$| ||= 133 973.33...| ||= 133 973 {{{suffix0}}}|
correctAnswer0
133973
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
correctAnswer0133973

cm3^3

Tags

  • ms_ca