Processing math: 100%

User interface language: English | Español

Date May 2018 Marks available 7 Reference code 18M.1.SL.TZ2.S_4
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number S_4 Adapted from N/A

Question

The following diagram shows a circle with centre O and radius r cm.

The points A and B lie on the circumference of the circle, and AOB = θ. The area of the shaded sector AOB is 12 cm2 and the length of arc AB is 6 cm.

Find the value of r.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

evidence of correctly substituting into circle formula (may be seen later)      A1A1
eg  12θr2=12,rθ=6

attempt to eliminate one variable      (M1)
eg  r=6θ,θ=1r,12θr2rθ=126

correct elimination      (A1)
eg  12×6r×r2=12,12θ×(6θ)2=12,A=12×r2×lr,r22r=2

correct equation     (A1)
eg  12×6r=12,12×36θ=12,12=12×r2×6r

correct working      (A1)
eg  3r=12,18θ=12,r2=2,24=6r

r = 4 (cm)      A1 N2

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.4—Circle: radians, arcs, sectors
Show 57 related questions
Topic 3— Geometry and trigonometry

View options