Question

1. circle y has a central angle, \\( \angle xyz \\), which is 90 degrees and forms the shaded segment shown. if the radius of the circle is 8 cm, what is the area of the shaded segment? write your answer in simplest \\( \pi \\) form.

Explanation:

Step1: Calculate the area of the sector

The formula for the area of a sector is \(A_{sector}=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta = 90^{\circ}\) and \(r = 8\) cm.

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Step2: Calculate the area of the triangle

The formula for the area of a right - angled triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). Here, base and height are equal to the radius \(r = 8\) cm.

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Step3: Calculate the area of the segment

The area of the segment \(A = A_{sector}-A_{triangle}\)

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Answer:

\(16\pi - 32\)