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

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Question 10

A mechanical component for a precision pendulum clock is designed using a triangular metal plate OAB OAB\,OAB attached to a weighted circular sector OBC OBC\,OBC with centre OOO.

In this design:

  • OB=6.5 cmOB = 6.5\text{ cm}OB=6.5 cm
  • AB=3.5 cmAB = 3.5\text{ cm}AB=3.5 cm
  • angle AOB=π12\displaystyle AOB = \frac{\pi}{12}AOB=12π​ radians
  • angle OAB OAB\,OAB is an obtuse angle
a.

Determine the size of angle OABOABOAB, giving your answer in radians to 4 significant figures.

[3]
b.

Calculate the area of the triangular plate OAB OAB\,OAB in cm2\text{cm}^2cm2, giving your answer to 3 significant figures.

[2]
c.

Given that the ratio of the area of the weighted sector OBC OBC\,OBC to the area of the triangular plate OAB OAB\,OAB is 7:4 7:4\,7:4

Show that angle BOC BOC\,BOC is 0.224 radians to 3 significant figures.

[3]
d.

Hence find the total perimeter of the component, in cm, to the nearest integer.

[3]

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

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