(a)[5]
With $\theta = 1.2$, work out the area of the metal plate. Give your answer correct to $3$ significant figures.
(b)[5]
If the area of each semicircle is $50\pi\text{ cm}^2$ instead, find the exact perimeter of the metal plate.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts a metal plate $ABCDEF$ formed from five regions. Regions $BCD$ and $DEF$ are semicircles. Region $BAFO$ is a sector of a circle with centre $O$ and radius $20\text{ cm}$. $D$ is located on this circle. Regions $OBD$ and $ODF$ are triangles. The angles $BOD$ and $DOF$ are each $\theta$ radians.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculating the area of sector $BOF$ as $\frac12\times20^2(2\pi-2.4)$ or an equivalent form.” …
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