Measurement, NAPX-H4-CA32 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

780

Question

Mickey cuts a quarter circle out of a full circle, as shown below.



If the circle's radius is 7 cm, what is the perimeter of the shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (34×2×π\bigg( \dfrac{3}{4} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (34×2×π\bigg(\dfrac{3}{4} \times 2 \times \large \pi × 7)+2×7\times\ 7 \bigg) + 2 \times 7
= 46.986...
= 47 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Mickey cuts a quarter circle out of a full circle, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/04/NAPX-H4-CA32.svg 200 indent vpad
If the circle's radius is 7 cm, what is the perimeter of the shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{3}{4} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{3}{4} \times 2 \times \large \pi$ $\times\ 7 \bigg) + 2 \times 7$| ||= 46.986...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
47
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
correctAnswer047

cm

Variant 1

DifficultyLevel

782

Question

Vinnie cuts away two-thirds of a circle, leaving the shape shown below.



If the circles' radius is 10 cm, what is the perimeter of the remaining shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (13×2×π\bigg( \dfrac{1}{3} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (13×2×π\bigg(\dfrac{1}{3} \times 2 \times \large \pi × 10)+2×10\times\ 10 \bigg) + 2 \times 10
= 40.9439...
= 41 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Vinnie cuts away two-thirds of a circle, leaving the shape shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-H4-CA32-SA_1.svg 200 indent vpad
If the circles' radius is 10 cm, what is the perimeter of the remaining shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{1}{3} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{1}{3} \times 2 \times \large \pi$ $\times\ 10 \bigg) + 2 \times 10$| ||= 40.9439...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
41
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
correctAnswer041

cm

Variant 2

DifficultyLevel

784

Question

Milo cuts away one third of a circle, leaving the shape shown below.



If the circle's radius is 5 cm, what is the perimeter of the remaining shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (23×2×π\bigg( \dfrac{2}{3} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (23×2×π\bigg(\dfrac{2}{3} \times 2 \times \large \pi × 5)+2×5\times\ 5 \bigg) + 2 \times 5
= 30.94...
= 31 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Milo cuts away one third of a circle, leaving the shape shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-H4-CA32-SA_2.svg 300 indent vpad
If the circle's radius is 5 cm, what is the perimeter of the remaining shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{2}{3} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{2}{3} \times 2 \times \large \pi$ $\times\ 5 \bigg) + 2 \times 5$| ||= 30.94...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
31
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
correctAnswer031

cm

Variant 3

DifficultyLevel

783

Question

Morris cuts a sector measuring 30 degrees from a full circle, as shown below.



If the circle's radius is 20 cm, what is the perimeter of the shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (30360×2×π\bigg( \dfrac{30}{360} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (112×2×π\bigg(\dfrac{1}{12} \times 2 \times \large \pi × 20)+2×20\times\ 20 \bigg) + 2 \times 20
= 50.471...
= 50 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Morris cuts a sector measuring 30 degrees from a full circle, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-H4-CA32-SA_3.svg 240 indent vpad
If the circle's radius is 20 cm, what is the perimeter of the shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{30}{360} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{1}{12} \times 2 \times \large \pi$ $\times\ 20 \bigg) + 2 \times 20$| ||= 50.471...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
50
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
correctAnswer050

cm

Variant 4

DifficultyLevel

784

Question

Morris cuts a sector measuring 60 degrees from a full circle, as shown below.



If the circle's radius is 36 cm, what is the perimeter of the shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (60360×2×π\bigg( \dfrac{60}{360} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (16×2×π\bigg(\dfrac{1}{6} \times 2 \times \large \pi × 36)+2×36\times\ 36 \bigg) + 2 \times 36
= 109.699...
= 110 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Morris cuts a sector measuring 60 degrees from a full circle, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-H4-CA32-SA_5.svg 210 indent vpad
If the circle's radius is 36 cm, what is the perimeter of the shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{60}{360} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{1}{6} \times 2 \times \large \pi$ $\times\ 36 \bigg) + 2 \times 36$| ||= 109.699...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
110
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
correctAnswer0110

cm

Variant 5

DifficultyLevel

777

Question

Monica cuts a right-angled sector from a full circle, as shown below.



If the circle's radius is 25 cm, what is the perimeter of the shape, to the nearest centimetre?

Worked Solution
Perimeter = arc + 2 × radii
= (14×2×π\bigg( \dfrac{1}{4} \times 2 \times \large \pi × r\times\ \large r )+2r\bigg) + 2\large r
= (14×2×π\bigg(\dfrac{1}{4} \times 2 \times \large \pi × 25)+2×25\times\ 25 \bigg) + 2 \times 25
= 89.2699...
= 89 cm (nearest cm)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Monica cuts a right-angled sector from a full circle, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_J-NAPX-H4-CA32-SA_4.svg 170 indent vpad
If the circle's radius is 25 cm, what is the perimeter of the shape, to the nearest centimetre?
workedSolution
||| |-|-| |Perimeter|= arc + 2 × radii| ||= $\bigg( \dfrac{1}{4} \times 2 \times \large \pi$ $\times\ \large r$ $\bigg) + 2\large r$| ||= $\bigg(\dfrac{1}{4} \times 2 \times \large \pi$ $\times\ 25 \bigg) + 2 \times 25$| ||= 89.2699...| ||= {{{correctAnswer0}}} {{{suffix0}}} (nearest cm)|
correctAnswer0
89
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
correctAnswer089

cm

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