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Arc Length, Sector Area and Radian Measure

Secondary 3 practice

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Arc Length, Sector Area and Radian Measure practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Arc Length, Sector Area and Radian Measure free

What this topic covers

Worked examples

Example 1

The perimeter of a sector OABOAB is 4444 m. The radius of the circle is 1313 m. Find the angle ∠AOB\angle AOB in radians, correct to 3 significant figures.
θ13 mOABNot drawn to scale
Show the worked solution
  • Perimeter of sector=rθ+2rperimeter formula\text{Perimeter of sector} = r\theta + 2r \quad \scriptsize\textit{perimeter formula}
  • =r(θ+2)= r(\theta + 2)
  • 44=13θ+2×1344 = 13\theta + 2 \times 13
  • 44=13θ+2644 = 13\theta + 26
  • 13θ=44−26subtract 2r13\theta = 44 - 26 \quad \scriptsize\textit{subtract } 2r
  • 13θ=1813\theta = 18
  • θ=1813divide by r\theta = \dfrac{18}{13} \quad \scriptsize\textit{divide by } r
  • θ=1.38\theta = 1.38 rad (to 3 s.f.)

Answer: 1.381.38

Example 2

Find the area of a sector of a circle with radius 2525 cm and sector angle π\pi radians. Give your answer correct to 3 significant figures.
π rad25 cmOABNot drawn to scale
Show the worked solution
  • Area of sector=12r2θradian formula\text{Area of sector} = \dfrac{1}{2} r^2 \theta \quad \scriptsize\textit{radian formula}
  • =12×252×π= \dfrac{1}{2} \times 25^2 \times \pi
  • =12×625×π= \dfrac{1}{2} \times 625 \times \pi
  • =312.5×π= 312.5 \times \pi
  • =982= 982 cm² (to 3 s.f.)

Answer: 982982

Example 3

Using your calculator in radian mode, find the value of tan⁡19π12\tan \dfrac{19\pi}{12}, correct to 3 significant figures.
Show the worked solution
  • Set calculator to radian mode.\text{Set calculator to radian mode.}
  • tan⁡ 19π12=−3.73 (to 3 s.f.)\tan\, \dfrac{19\pi}{12} = -3.73 \text{ (to 3 s.f.)}

Answer: −3.73-3.73

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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