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 between degrees and radians and use radian measure consistently in exact or decimal angle calculations.
Calculate arc length and sector area with s = rθ and A = ½r²θ, identifying the radius and central angle in radians.

[Maximum number: 3]

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