The diagram shows the arcs $AD$ and $BC$ of two circles with centre $O$. The length of arc \(A

Question

The diagram shows the arcs $AD$ and $BC$ of two circles with centre $O$. The length of arc $AD$ is $8\pi$ cm and the length of $DC$ is $12$ cm. $OAB$ and $ODC$ are straight lines and $\angle AOD = \frac{\pi}{4}$ radians. Show that the radius of the sector $OAD$ is $32$ cm. Leaving your answers in terms of $\pi$, find the perimeter of the shaded region. area of the shaded region.

Accepted Answer

(i) $32\text{ cm}$ (ii)(a) $(24+19\pi)\text{ cm}$ (ii)(b) $114\pi\text{ cm}^2$

Introduction to Circular Measure: Arc Length and Sector Area

Introduction to Circular Measure: Arc Length and Sector Area

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