Calculate the area of sectors and segments of a circle, and apply these to real-world problems involving combinations of circular shapes.
Sector area = (θ/360°)×πr². Segment area = sector area − triangle area (formed by the two radii and chord).
Find the area of a sector with radius 14cm and angle 90° (π=22/7).
(90/360)×22/7×196=154 cm²
Find the area of a segment with radius 10cm, angle 90°, given the sector area is 78.5 cm² and triangle area is 50 cm² (using π=3.14).
78.5-50=28.5 cm²
Many problems involve combining or subtracting circular areas — like rings, or a square with circles removed.
A ring has outer radius 7cm and inner radius 3.5cm. Find its area (π=22/7).
22/7×(49-12.25)=22/7×36.75=115.5 cm²
A square of side 14cm has a circle of radius 7cm inscribed. Find the area outside the circle but inside the square (π=22/7).
196-154=42 cm²
1. Find the area of a sector with radius 21cm and angle 60° (π=22/7).
2. Find the area of a sector with radius 7cm and angle 120° (π=22/7).
3. A ring has outer radius 10cm and inner radius 6cm. Find its area (π=3.14).
4. A circle of radius 7cm is inscribed in a square. Find the area outside the circle (π=22/7).
5. Find the circumference of a circle with area 154 cm² (π=22/7).