Question 40

If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10$$\pi$$, then the area of the sector XYZ is

Solution

Length of arc XZ is the perimeter of quarter circle.

$$\frac{\pi r}{2}$$ = 10$$\pi$$

r=20

Area of sector XYZ = Area of quarter circle = $$\frac{\pi r^{2}}{4}$$

Area = 100$$\pi$$

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