Measurement, NAPX-p169635v01

Question

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Worked Solution

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Variant 0

DifficultyLevel

542

Question

Two circles have radii of different lengths.



The larger circle’s radius is 3.5 times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

Worked Solution
Large radius = 6 × 3.5
= 21 cm
∴\therefore Circumference = 2 × π\large \pi × RR
= 2 × π\large \pi × 21
= 42π\large \pi cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two circles have radii of different lengths.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2021/05/RAPH10_62.svg 280 indent vpad
The larger circle’s radius is 3.5 times the radius of the smaller circle. Which of the following is the circumference of the larger circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 6 × 3.5 | | | \= 21 cm |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $R$ | | | \= 2 × $\large \pi$ × 21 | || \= {{{correctAnswer}}}|
correctAnswer
42$\large \pi$ cm

Answers

Is Correct?Answer
x

56π\large \pi cm

✓

42π\large \pi cm

x

40π\large \pi cm

x

36π\large \pi cm

Variant 1

DifficultyLevel

541

Question

Two circles have radii of different lengths.



The larger circle’s radius is 1.5 times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

Worked Solution
Large radius = 4 × 1.5
= 6 cm
∴\therefore Circumference = 2 × π\large \pi × RR
= 2 × π\large \pi × 6
= 12π\large \pi cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two circles have radii of different lengths.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-p169635v01_v1a.svg 330 indent3 vpad
The larger circle’s radius is 1.5 times the radius of the smaller circle. Which of the following is the circumference of the larger circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 4 × 1.5 | | | \= 6 cm |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $R$ | | | \= 2 × $\large \pi$ × 6 | || \= {{{correctAnswer}}}|
correctAnswer
12$\large \pi$ cm

Answers

Is Correct?Answer
✓

12π\large \pi cm

x

16π\large \pi cm

x

20π\large \pi cm

x

36π\large \pi cm

Variant 2

DifficultyLevel

540

Question

Two circles have radii of different lengths.



The larger circle’s radius is 2.5 times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

Worked Solution
Large radius = 10 × 2.5
= 25 m
∴\therefore Circumference = 2 × π\large \pi × RR
= 2 × π\large \pi × 25
= 50π\large \pi m

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two circles have radii of different lengths.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-p169635v01_v2a.svg 400 indent vpad
The larger circle’s radius is 2.5 times the radius of the smaller circle. Which of the following is the circumference of the larger circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 10 × 2.5 | | | \= 25 m |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $R$ | | | \= 2 × $\large \pi$ × 25 | || \= {{{correctAnswer}}}|
correctAnswer
50$\large \pi$ m

Answers

Is Correct?Answer
x

20π\large \pi m

x

25π\large \pi m

✓

50π\large \pi m

x

100π\large \pi cm

Variant 3

DifficultyLevel

545

Question

Two circles have radii of different lengths.



The smaller circle’s radius is one quarter the radius of the larger circle.

Which of the following is the circumference of the smaller circle?

Worked Solution
Large radius = 12 × 0.25
= 3 cm
∴\therefore Circumference = 2 × π\large \pi × rr
= 2 × π\large \pi × 3
= 6π\large \pi cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two circles have radii of different lengths.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-p169635v01_v3a_2.svg 330 indent vpad
The smaller circle’s radius is one quarter the radius of the larger circle. Which of the following is the circumference of the smaller circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 12 × 0.25 | | | \= 3 cm |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $r$ | | | \= 2 × $\large \pi$ × 3 | || \= {{{correctAnswer}}}|
correctAnswer
6$\large \pi$ cm

Answers

Is Correct?Answer
✓

6π\large \pi cm

x

12π\large \pi cm

x

24π\large \pi cm

x

36π\large \pi cm

Variant 4

DifficultyLevel

546

Question

Two circles have radii of different lengths.



The smaller circle’s radius is two-thirds the radius of the larger circle.

Which of the following is the circumference of the smaller circle?

Worked Solution
Large radius = 15 × 23\dfrac{2}{3}
= 10 cm
∴\therefore Circumference = 2 × π\large \pi × r\large r
= 2 × π\large \pi × 10
= 20π\large \pi cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two circles have radii of different lengths.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-p169635v01_v4a_2.svg 360 indent vpad
The smaller circle’s radius is two-thirds the radius of the larger circle. Which of the following is the circumference of the smaller circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 15 × $\dfrac{2}{3}$ | | | \= 10 cm |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $\large r$ | | | \= 2 × $\large \pi$ × 10 | || \= {{{correctAnswer}}}|
correctAnswer
20$\large \pi$ cm

Answers

Is Correct?Answer
x

10π\large \pi cm

x

15π\large \pi cm

✓

20π\large \pi cm

x

30π\large \pi cm

Variant 5

DifficultyLevel

545

Question

Two concentric circles are shown below.



The larger circle’s radius is one and one-third times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

Worked Solution
Large radius = 21 × 43\dfrac{4}{3}
= 28 cm
∴\therefore Circumference = 2 × π\large \pi × RR
= 2 × π\large \pi × 28
= 56π\large \pi cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Two concentric circles are shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement_NAPX-p169635v01_v5a.svg 330 indent vpad
The larger circle’s radius is one and one-third times the radius of the smaller circle. Which of the following is the circumference of the larger circle?
workedSolution
| | | | --------------------- | -------------- | | Large radius | \= 21 × $\dfrac{4}{3}$ | | | \= 28 cm |
| | | | --------------------- | -------------- | | $\therefore$ Circumference| \= 2 × $\large \pi$ × $R$ | | | \= 2 × $\large \pi$ × 28 | || \= {{{correctAnswer}}}|
correctAnswer
56$\large \pi$ cm

Answers

Is Correct?Answer
x

14π\large \pi cm

x

28π\large \pi cm

x

42π\large \pi cm

✓

56π\large \pi cm

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