IB Maths AA HL Sl 3 4 Radian Measure Questions

Practise converting degrees to radians, using s = rθ and sector or segment formulae, and solving circular geometry or physical models with correct units.

Exam points

Convert an angle between degrees and radians, giving an exact multiple of Ï€ or an appropriately rounded value.
Use s=rÎ¸ to calculate an arc length or recover a radius/angle from a stated arc and unit.
Use sector and segment formulae to find area or perimeter, including shaded regions made from circles, sectors, chords and triangles.
Translate a radian-based geometric or physical model into equations, solve for the required parameter and check units/precision.

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Study SL 3.4—Radian measure conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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The points A and B lie on a circle, with centre O and radius 19.5 cm , such that $\mathrm{BO} \widehat{\mathrm{O}}=210^{\circ}$ .
A piece of paper is cut into the shape of the sector BOA .
A hollow cone with no base is constructed from the sector by joining the points A and B . The sector forms the curved surface of the cone.
This is shown in the following diagrams.

Figure for Question IB Maths AA HL Sl 3 4 Radian Measure Questions question 1 — IB Maths AA HL

Find

the area of the sector BOA ;

EITHER
$210^{\circ}=\frac{210 \pi}{180}\left(=\frac{7 \pi}{6}=3.66519 \ldots\right)$ radians
attempt to use radian formula for area of sector
area $=\frac{1}{2}(19.5)^{2}\left(\frac{7 \pi}{6}\right)$
OR
attempt to use degree formula for area of sector
area $=\frac{210}{360} \pi(19.5)^{2}$

THEN
area $=\frac{3549 \pi}{16}=696.844 \ldots$ $=697\left(=\frac{3549 \pi}{16}\right)\left(\mathrm{cm}^{2}\right)$

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IB Maths AA HL Sl 3 4 Radian Measure Questions question 1