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Radians

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Question 13

An artist is designing a corporate logo. The design consists of a sector DOCDOCDOC of a circle with centre OOO and radius ODODOD. This is joined to a major sector AOBEAAOBEAAOBEA of a smaller circle, also with centre OOO and radius OAOAOA. The points AAA and BBB lie on the line segments ODODOD and OCOCOC respectively, such that OOO, AAA, DDD and OOO, BBB, CCC are collinear.

Given that:

  • angle AOB=0.82AOB = 0.82AOB=0.82 radians
  • arc length CD=20.5 cmCD = 20.5\text{ cm}CD=20.5 cm
  • the ratio of lengths DA:AO=7:3DA : AO = 7 : 3DA:AO=7:3
a.

Show that AO=7.5 cmAO = 7.5\text{ cm}AO=7.5 cm.

[3]
b.

Calculate the perimeter of the logo, in cm, to 3 significant figures.

[4]
c.

Calculate the total area of the logo, in cm2\text{cm}^2cm2, to the nearest whole number.

[3]
Markscheme

Radians Questions

  1. A Level
  2. /Maths
  3. /Radians

278 exam-style questions on Edexcel A Level Maths Radians, covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations. Each one has a worked solution and a mark scheme showing where the marks go.

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