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 $XE=0.2$” …