Edexcel IGCSE Math B 7.D arcs and sectors

Practise arcs-and-sectors questions by using the central angle as a fraction of 360 degrees before calculating length, area or perimeter.

Exam points

Calculate arc length or sector area from radius and central angle information.
Use sector perimeter by combining arc length with the two radii in the diagram.
Apply sector area in compound contexts such as grass seed or shaded regions.

[Maximum number: 3]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

Calculate the area, in $\mathrm{cm}^{2}$ to 3 significant figures, of the region shown shaded in Figure 3.
[Area of circle $=\pi r^{2}$ ]

Sector area:
$\frac{100}{360}\times\pi\times10^{2}=87.27\ldots$
Shaded region:
$119-87.27\ldots=31.7\ldots$
Final answer:
$31.7\text{ to }31.9\text{ cm}^{2}$

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7.D Arcs and sectors question 1