(a)[2]
Show that angle $PAQ$ is $\frac{1}{3}\pi$ radians.
(b)[4]
Find the rope's length.
(c)[2]
Find the area of the hexagon $ABCDEF$, and give your answer in terms of $\sqrt{3}$.
(d)[3]
Find the area of the whole region enclosed by the rope.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram presents a cross-section of seven cylindrical pipes, each with radius $20\text{ cm}$, secured by a thin rope that is pulled taut around them. The centres of the six outer pipes are $A, B, C, D, E$ and $F$. Points $P$ and $Q$ mark the places where the straight parts of the rope touch the pipe centred at $A$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid reasoning leading to $6\times \angle P\hat{A}Q=2\pi$” …
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