IB Maths AA HL 3.4 Radian measure Question Bank

Practise IB Mathematics SL/HL 3.4 by applying radian measure methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[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 SL 3.4—Radian measure 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 $=\frac{3549 \pi}{16}=696.844 \ldots$ $=697\left(=\frac{3549 \pi}{16}\right)\left(\mathrm{cm}^{2}\right)$

All question bank results loaded

SL 3.4—Radian measure question 1