In the diagram below, $APB$ is an arc of a circle centre $O$ and radius $5$ cm. $AQB$ is sem

Question

In the diagram below, $APB$ is an arc of a circle centre $O$ and radius $5$ cm. $AQB$ is semicircle with $AB$ as its diameter and $\angle AOB = \frac{4}{9}\pi$. Show that the length of $AB = 6.43$ cm. Calculate the length of the arc $APB$. Calculate the area of the semi-circle $AQB$. Calculate the area of the $\Delta AOB$ and hence, find the area of shaded region.

Accepted Answer

(i) $AB=6.43\text{ cm}$ (ii) $6.98\text{ cm}$ (iii) $16.2\text{ cm}^2$ (iv) Triangle $AOB$: $12.3\text{ cm}^2$ Shaded region: $11.1\text{ cm}^2$

Radian Measure: Arc Length and Sector Area

Radian Measure: Arc Length and Sector Area

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