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10.7 Areas of Circles and Sectors. The area of a circle is the product of pi and the square of the radius. Finding the Area of a Circle. The diameter of the circular region on the wrestling mat is 32 feet. What is the area?. Sector of a Circle. - PowerPoint PPT Presentation
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10.7 Areas of Circles and Sectors• The area of a circle is the product of pi and the
square of the radius.
2A r
Finding the Area of a Circle• The diameter of the circular region on the wrestling
mat is 32 feet. What is the area?
2A r2(16)A
256A 804.2477193
2804 .ft
Sector of a Circle• A sector of a circle is a region bounded by an arc of
the circle and the two radii to the arc’s endpoints.– You name a sector using one arc endpoint, the center of
the circle, and the other arc endpoint.
Area of a Sector of a Circle• The area of a sector of a circle is the product of the
radio measure of the arc : 360 and the area of the circle.
Finding the Area of a Sector of a Circle• What is the area of sector GPH? Leave your answer
in terms of pi.
2sec
360
mGHareaof torGPH r
272(15)
360
245 cm
Segment of a Circle
• A part of a circle bounded by an arc and the segment joining its endpoints is a segment of a circle.
• To find the area of a segment for a minor arc, draw radii to form a sector.
• The area of the segment equals the area of the sector minus the area of the triangle formed.
Finding the Area of a Segment of a Circle
• What is the area of the shaded segment shown? Round your answer to the nearest tenth.
Finding the Area of a Segment of a Circle
2sec360
mABAreaof torACB r
260(18)
360
541
2areaof ABC bh
1(18)(9 3)2
81 3
54 81 3areaofshadedsegment 29.34988788
229.3 .in
More Practice!!!!!
• Homework – Textbook p. 663 – 664 # 7 – 25 ALL.