IB Questionbank

User interface language: English | Español

Date	May 2008	Marks available	2	Reference code	08M.2.sl.TZ1.3
Level	SL only	Paper	2	Time zone	TZ1
Command term	Find	Question number	3	Adapted from	N/A

Question

The diagram below shows a circle centre O, with radius r. The length of arc ABC is $3\pi {\text{ cm}}$ and ${\rm{A}}\widehat {\rm{O}}{\rm{C}} = \frac{{2\pi }}{9}$ .

Find the value of r.

[2]

Find the perimeter of sector OABC.

[2]

Find the area of sector OABC.

[2]

Markscheme

evidence of appropriate approach M1

e.g. $3\pi = r\frac{{2\pi }}{9}$

$r = 13.5$ (cm) A1 N1

[2 marks]

adding two radii plus $3\pi$ (M1)

${\text{perimeter}} = 27 + 3\pi$ (cm) ( $= 36.4$ ) A1 N2

[2 marks]

evidence of appropriate approach M1

e.g. $\frac{1}{2} \times {13.5^2} \times \frac{{2\pi }}{9}$

area $= 20.25\pi$ ( ${\text{cm}}^2$ ) ( $= 63.6$ ) A1 N1

[2 marks]

Examiners report

Few errors were made in this question. Those that were made were usually arithmetical in nature.

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.1 » The circle: radian measure of angles; length of an arc; area of a sector.

Show 43 related questions

17N.1.sl.TZ0.4b: The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the...
17N.1.sl.TZ0.4a: Show that ${\text{AC}} = 7{\text{ cm}}$ .
16M.1.sl.TZ2.5b: Find the exact area of the sector BDC.
16M.1.sl.TZ2.5a: Find ${\rm{A\hat BC}}$ .
16N.2.sl.TZ0.3b: Find the value of $r$ .
16N.2.sl.TZ0.3a: Write down the exact value of $\theta$ in radians.
12N.2.sl.TZ0.8a: Find the length of the chord [AB].
12N.2.sl.TZ0.8b: Find the area of triangle AOB.
12N.2.sl.TZ0.8c: Angle BOC is 2.4 radians. Find the length of arc ADC.
12N.2.sl.TZ0.8d: Angle BOC is 2.4 radians. Find the area of the shaded region.
12N.2.sl.TZ0.8e: Angle BOC is 2.4 radians. The shaded region is to be painted red. Red paint is sold in cans...
12M.2.sl.TZ2.10a: Use the cosine rule to show that ${\rm{PQ}} = 2r\sin \theta$ .
12M.2.sl.TZ2.10c(i) and (ii): Consider the function $f(\theta ) = 2.6\sin \theta - 2\theta$ , for...
12M.2.sl.TZ2.10d: Use the graph of f to find the values of $\theta$ for which $l < 1.3{\rm{PQ}}$ .
12M.2.sl.TZ2.10b: Let l be the length of the arc PRQ . Given that $1.3{\rm{PQ}} - l = 0$ , find the value of...
08M.2.sl.TZ1.3a: Find the value of r.
08M.2.sl.TZ1.3b: Find the perimeter of sector OABC.
12M.2.sl.TZ1.9a(i) and (ii): (i) Show that ${p^2}(41 - 40\cos 0.7) = 36$ . (ii) Find p .
12M.2.sl.TZ1.9b: Write down the length of BD.
12M.2.sl.TZ1.9c: Find ${\rm{A}}\widehat {\rm{D}}{\rm{B}}$ .
12M.2.sl.TZ1.9d(i) and (ii): (i) Show that ${\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29$ radians, correct to 2 decimal...
10N.1.sl.TZ0.3a: Find the length of the arc ACB .
10N.1.sl.TZ0.3b: Find the area of the shaded region.
09N.2.sl.TZ0.8c: Find the area of sector OABC.
09M.2.sl.TZ1.2b: Find the area of the shaded region.
10M.2.sl.TZ2.8a: Find the size of angle AOC .
10M.2.sl.TZ2.8d: Find EF .
10M.2.sl.TZ2.8b: Hence find the area of the shaded region.
10M.2.sl.TZ2.8c: The area of sector OCDE is $45{\text{ c}}{{\text{m}}^2}$ . Find the size of angle COE .
SPNone.2.sl.TZ0.7a: Find an expression for the area of the shaded region.
11N.2.sl.TZ0.3a: Find the value of $\theta$ .
11N.2.sl.TZ0.3b: Find the area of the shaded region.
13M.2.sl.TZ2.7b: The area of the shaded region is $25$ cm2 . Find the value of $r$ .
14M.2.sl.TZ2.1a(i): Find the length of the arc ${\text{ABC}}$ .
14M.2.sl.TZ2.1a(ii): Find the perimeter of the shaded sector.
14M.2.sl.TZ2.1b: Find the area of the shaded sector.
13N.2.sl.TZ0.8c: Hence or otherwise, find the length of arc ${\text{ABC}}$ .
15M.1.sl.TZ1.2a: Find the length of ${\text{arc ACB}}$ .
15M.1.sl.TZ1.2b: Find the perimeter of the shaded region.
15M.2.sl.TZ2.10b: When $\theta = \alpha$ , the area of the square $ABCD$ is equal to the area of the...
14N.2.sl.TZ0.3a: Find the length of arc $ACB$ .
15N.2.sl.TZ0.1a: Find the length of arc $ABC$ .
15N.2.sl.TZ0.1b: Find the area of the shaded region.

Hide related questions

Question

Markscheme

Examiners report

Syllabus sections

View options