In the diagram, the square $PQRS$ is inscribed in the sector $OAB$ of a circle, with centre \(O\

Question

In the diagram, the square $PQRS$ is inscribed in the sector $OAB$ of a circle, with centre $O$ and radius $8$ cm. Given that $\angle AOB = 45^\circ$, $OS = OR = 5$ cm, find the length of $SR$, the arc length $PQ$, the area of the shaded region.

Accepted Answer

(i) $SR=3.83\text{ cm}$. Parts (ii)–(iii): inconsistent givens; the square forces radius $5\sqrt3\text{ cm}$, not $8\text{ cm}$.

IP2U13 13.4 PN1 Q13

IP2U13 13.4 PN1 Q13

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