CAIE A-Level Mathematics 1.4.2 Arc Length and Sector Area

Practise applying s = rθ and A = ½r²θ to sectors and compound figures, using triangle geometry to obtain unknown angles, radii, perimeters and segment areas.

Exam points

calculate arc length with s = rθ and add radial or chord lengths for a perimeter
calculate sector area with A = ½r²θ and subtract or add the relevant triangle area
derive an unknown r or θ from area or perimeter data before giving an exact final result

[Maximum number: 2]

Figure for Question 1.4.2—Arc length and sector area question 1 — CAIE A-Level Mathematics AS

The diagram shows a sector of a circle with centre O and radius $r \mathrm{~cm}$ . The shaded region is bounded by the chord AB and the $\operatorname{arc} A B$ . The size of angle AOB is $\frac{2}{3} \pi$ radians.

Show that the area of the shaded region is approximately $0.614 r^{2} \mathrm{~cm}^{2}$ .

It is given that the radius of the circle is increasing at a rate of $0.4 \mathrm{~cm} \mathrm{~s}^{-1}$ .

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1.4.2—Arc length and sector area question 1