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Radians

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Question 36

The diagram shows the design for a decorative glass panel in the shape of a semicircle with center O O\,O and diameter AOEAOEAOE. The points B B\,B and D D\,D lie on the arc of the semicircle such that the chord BD BD\,BD is parallel to the diameter AEAEAE. A specific section of the glass, a segment labeled RRR, is bounded by the chord BD BD\,BD and the arc BCDBCDBCD. The radius of the semicircle is 8 cm and the angle DOE DOE\,DOE is 0.45 radians.

Semicircular glass panel with diameter AOE, horizontal chord BD, centre O, angle DOE of 0.45 radians, radius 8 cm, and shaded segment R bounded by chord BD and arc BCD.

a.

Show that, to 3 decimal places, the angle BOD BOD\,BOD is 2.242 radians.

[3]
b.

Find the area of the shaded glass segment RRR, giving your answer in cm2\text{cm}^2cm2 to one decimal place.

[3]
c.

Find the perimeter of the shaded region RRR, giving your answer in cm\text{cm}cm to one decimal place.

[4]
Markscheme

Radians Questions

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

69 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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