Mathematics 9709 · AS & A Level · Circular measure

Circular measure — practice question

The diagram depicts a symmetric plate $ABCDEF$. The line $ABCD$ is straight, and $BC$ measures $2\text{ cm}$. The two sectors $ABF$ and $DCE$ each have radius $r\text{ cm}$, and each angle $ABF$ and $DCE$ is $\frac{1}{3}\pi$ radians.
(a(i))[2]

You are told that $r = 0.4\text{ cm}$. Prove that $EF = 2.4\text{ cm}$.

(a(ii))[4]

Find the area of the plate, giving your answer correct to $3$ significant figures.

(b)[4]

Now suppose the perimeter of the plate is $6\text{ cm}$. Determine the value of $r$, with your answer correct to $3$ significant figures.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Uses a trig ratio to obtain $XE=0.2$

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