Measurement, NAPX-E4-NC32 SA

Question

Two circles have the same centre, OO, as shown in the diagram below.

The radius of the small circle is 34\dfrac{3}{4} the radius of the large circle.

Arc CDCD is 24 mm and the angle between the lines ACAC and BD is 30°\degree.

What is the length of the arc RSRS in millimetres?

Worked Solution
Arc STST = 34 ×arc  CD\dfrac{3}{4}\ \times \text{arc}\ \ CD
= 34×24\dfrac{3}{4} \times 24
= 18 mm

∠\angleSOR = 180−30180 - 30
= 150°150\degree
= 5 ×\times ∠\angleSOT

∴Arc RS\therefore \text{Arc}\ RS = 5×185 \times 18
= {{{correctAnswer0}}} {{{suffix0}}}

Variant 0

DifficultyLevel

727

Question

Two circles have the same centre, OO, as shown in the diagram below.

The radius of the small circle is 34\dfrac{3}{4} the radius of the large circle.

Arc CDCD is 24 mm and the angle between the lines ACAC and BD is 30°\degree.

What is the length of the arc RSRS in millimetres?

Worked Solution
Arc STST = 34 ×arc  CD\dfrac{3}{4}\ \times \text{arc}\ \ CD
= 34×24\dfrac{3}{4} \times 24
= 18 mm

∠\angleSOR = 180−30180 - 30
= 150°150\degree
= 5 ×\times ∠\angleSOT

∴Arc RS\therefore \text{Arc}\ RS = 5×185 \times 18
= 90 mm

Question Type

Answer Box

Variables

Variable nameVariable value
correctAnswer0
90
prefix0
suffix0
mm

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
correctAnswer090

mm

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