CAIE IGCSE Additional Math 9.1 arc length and sector area

Use this arcs-and-sectors page to convert angle information into radians, calculate sector areas and combine regions for exact shaded areas.

Exam points

Find arc lengths and sector areas using angles in radians and exact formulae.
Calculate exact shaded areas by combining sectors, triangles and circular regions.
Use geometry facts to find angles such as AQB before applying sector formulae.

[Maximum number: 3]

A circle, centre O and radius $r\text{ cm}$ , has a sector OAB of fixed area $10\text{ cm}^2$ . Angle AOB is $\theta$ radians and the perimeter of the sector is $P\text{ cm}$ .

Find an expression for P in terms of r.

$\frac12r^2\theta=10,\quad \theta=\frac{20}{r^2}$
B1
$P=2r+r\theta$
M1
$P=2r+\frac{20}{r}$
A1

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9.1. Solve arc length and sector area problems question 1