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Geometric Analysis: Relationships Between Central Angles, Arc Length, and Area

Geometric Analysis: Relationships Between Central Angles, Arc Length, and Area

TGM Original

The diagram shows a sector \(POQ\) of a circle.
The radius of the sector is \(32\) cm and the angle is \(135{}^\circ \).

  1. Calculate the arc \(PQ\) in terms of \(\pi\).

The sector is used to make a hollow cone by joining the edges \(OP\) and \(OQ\).

  1. Calculate
    1. the radius of the base of the cone.
    2. the curved surface area of the cone, giving your answer in terms of \(\pi\).

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Answer:(a) \(24\pi\text{ cm}\) (b)(i) \(12\text{ cm}\) (b)(ii) \(384\pi\text{ cm}^2\)

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