Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths OCR (MEI)
  5. Question bank

1.7.13 Arc length and area of a sector (A-level only)

MediumHard
1234
Question 1

An architectural blueprint for a plaza features a circular water fountain and a stone promenade. The fountain area is defined by a major sector ABCOAABCOAABCOA of a circle with centre OOO, while the promenade is a triangle AODAODAOD adjacent to it. The following information is given:

  • The radius of the fountain is OA=OC=12 mOA = OC = 12\text{ m}OA=OC=12 m
  • The edge of the promenade ADADAD has a length of 25 m25\text{ m}25 m
  • The angle ∠ODA\angle ODA∠ODA at the far end of the promenade is 0.35 radians0.35\text{ radians}0.35 radians
  • The angle ∠AOD\angle AOD∠AOD is obtuse
  • The points OOO, CCC, and DDD lie on a straight line

The major sector ABCOAABCOAABCOA has an arc ABCABCABC that starts at CCC and ends at AAA.

Find:

a.

the size of angle ∠AOD\angle AOD∠AOD, in radians, to 3 decimal places,

[3]
b.

the length of the arc ABCABCABC of the fountain, in metres, to one decimal place,

[2]
c.

the total area of the plaza feature (fountain and promenade), in m2\text{m}^2m2, to one decimal place.

[4]

1.7.13 Arc length and area of a sector (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.7.13 Arc length and area of a sector (A-level only)