Working with  Sectors and Segments Topic Index | Geometry Index | Regents Exam Prep Center
 Answer the following questions dealing with the Sectors and Segments of Circles. (Do not assume that diagrams are drawn to scale.)
 1. Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to the nearest tenth of a square unit. Choose: 0.3 sq. units 15.7 sq. units 19.7 sq. units 50.3 sq. units. Explanation Determine the fractional part of the area needed. Form a fraction of the arc length to the total circumference. Area of sector = 7.85/(2•pi•r) • area of circle

 2. Find the area of the shaded sector of circle O.  The radius is 6 inches and the central angle is 100°.  Express answer to the nearest tenth of a square inch. Choose: 5.2 sq. in.  10.5 sq. in. 31.4 sq. in. 62.8 sq. in. Explanation Find frational portion of the circle by using 100/360. Area of sector = 100/360 • (pi) • 6² Area of sector = 31.4 square inches

 3. Find the area of the shaded segment of circle O to the nearest tenth of a square unit.  The radius of the circle is 6 units.  The perpendicular from O to the chord joining point A to point B measures 4 units. Choose: 4.8 sq. units 12.4 sq. units 30.3 sq. units 48.2 sq. units Explanation Find AP by using the Pythagorean Theorem. AP = 4.472135955 Find measure of angle AOP using trig. cos x = 4/6 measure angle AOP = 48.1896851º Area of sector = (2•48.189)/360 • (pi)36 = 30.27847214 Area triangle = (1/2) • 4 • (2•4.472135955) = 17.88854382 Area segment = Area sector - Area triangle = 12.4

 4. Pizza!  Pizza!  You stop for lunch at a local pizza shop where each pizza is cut into 8 slices.  Would your hunger be better satisfied with one slice from a 16 inch pizza or two slices from a 12 inch pizza (disregarding thickness)? Choose: 1 slice 2 slices Explanation The area of the larger slice is 25.13274123 sq. units. The area of one smaller slice is 14.13716694 sq. units. Two smaller slices has 28.27433388 sq. units = more pizza!!

 5. A cathedral window is built in the shape of a semicircle.  If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section?  Express answer to the nearest square foot. Choose: 1 sq, ft. 3 sq. ft. 13 sq. ft. 26 sq. ft. Explanation The radius of the circle is 2.5 feet. Each stained glass section is 1/6 of the circle. Area of the sector = 1/6 • (pi) • 2.5² = 3 sq. ft.

 6. Find the area of a segment of a circle if the central angle of the segment is 60° and the radius is 10.  Express answer to the nearest tenth of a square unit. Choose: 9.1 sq. units 27.2 sq. units 43.3 sq. units 52.4 sq. units Explanation Area of sector = 1/6 • pi • 10² = 52.359 Area of triangle = (10² radical 3)/4 = 43.301 Area of Segment = 52.359 - 43. 302 = 9.058 Area of segment = 9.1 sq. units.

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