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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 254

A motion-activated security sensor at a warehouse entrance sweeps a circular sector OABOABOAB with centre OOO. The sensor has a detection range of r=106 mr = 10\sqrt{6}\text{ m}r=106​ m and its field of vision is defined by the central angle AOB=π6AOB = \frac{\pi}{6}AOB=6π​ radians. A straight security barrier is installed on the floor connecting points AAA and BBB, creating a segment-shaped region between the barrier and the arc ABABAB.

Show that the area of this segment-shaped region is

k(π−3) m2 k(\pi - 3) \text{ m}^2 k(π−3) m2

where kkk is an integer to be found.

[4]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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