Pre-AP Geometry Worksheet 6.4

Pre-AP Geometry Name: ___________________ Worksheet 6.4 Date: _______ Period: ____ Find the area of the circle and the area of the sector requested. Show work. The center of each circle is O. Leave answers in exact form for problems 1 – 6.

1) Area = _________ 2) Area = _________ 3) Area= ____________ Area Sector AOB________ Area Sector AOB = _________ Area Sector AOB= ________

4) Length of AB=______ 5) Length of ACB = _____ 6) Length of ACB = _____ Area Sector AOB= ________ Area Shaded Sector = ________ Area Shaded Sector = ________

BO 6m

120

A

C

B

A

O

18m

C

40

Pre-AP Geometry Worksheet 6.4

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. 7) What is the approximate length of the arc of the section containing peas?

a) 3 in. b) 21 in. c) 16 in. d) 5 in.

8) What is the approximate area of the section of the plate containing peas?

a) 5 in2 b) 16 in2 c) 65 in2 d) 21 in2

9) The diameter of a small pizza is 10 inches. How much more pizza do you get if you order a medium pizza with diameter 12 inches? (Round answer to the nearest tenth of a square inch.) 10) Doris had a circular garden with a radius of 30 feet. She used all of the fencing from the circular garden to enclose a square garden. The length of each side of Doris’s square garden was approximately _____ feet.

47 feet B 94 feet C 120 feet D 188 feet

11) A 16-inch pizza is cut into eight equal sectors. Find the approximate area of one sector. Round answer to the nearest tenth of a square inch.

Pre-AP Geometry Worksheet 6.4

12) In the equation circumference = (pi)(diameter) or c = πd, which value represents the dependent variable, and which represents the independent variable?

Dependent variable ____________ Independent variable ____________ 13) Find the shaded area. 14) Find the shaded area. Leave answer in exact form. Leave answer in exact form. Shaded area _________ shaded area ______________ 15) The area of a sector of a circle is 36π square meters and has a 40° central angle associated with it. What is the radius of the circle? 16) The area of a sector of a circle is 48π square meters and has a 120° central angle associated with it. What is the radius of the circle?

°

° °

Pre-AP Geometry Worksheet 6.4

17) An 8-foot by 10-foot floating rectangular dock is anchored in the middle of the pond. The bow of a canoe is tied to one corner of the dock with a 10-foot rope. a) Use the diagram below and sketch the area in which the bow of the canoe can travel. The bow is the end attached by the rope. Pay attention to the dimensions of the figure. (Hint use a compass to draw the path the canoe can travel) (Assume that the rope does not go over the dock) b) Find the area. Round the area to the nearest square foot. KEY TO ODDS: 1) 144π m2; 12π m2 3) 100π m2; 30π m2 5) 32π m; 288π m2 7) D 9) 34.5 in2 11) 25.1 in2 13) (36π - 72) m2 15) 18 meters

PRACTICE and APPLICATION EXERCISES

ONLINE

HO M E W O R

K

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Find the area of each circle. Leave your answer in terms of P.

1. 2. 3.

Find the area of each shaded segment. Round your answer to the nearest tenth.

4. 5. 6.

7. Apply Mathematics (1)(A) Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an irrigation circle. How much land is covered with an irrigation arm of 300 ft?

Find the area of each shaded sector of a circle. Leave your answer in terms of P.

8. 9. 10. 11.

Find the area of the shaded region. Leave your answer in terms of P and in simplest radical form.

12. 13. 14. 15.

Find the area of sector TOP in O using the given information. Leave your answer in terms of P.

16. r = 5 m, mTP¬ = 90 17. d = 16 in., mPT¬ = 135

18. Apply Mathematics (1)(A) Refer to the diagram of the regular hexagonal nut. What is the area of the hexagonal face to the nearest square millimeter?

19. Create Representations to Communicate Mathematical Ideas (1)(E) Draw a circle and a sector so that the area of the sector is 16p cm2. Give the radius of the circle and the measure of the sector’s arc.

20. Analyze Mathematical Relationships (1)(F) AB and CD are diameters of }O. Is the area of sector AOC equal to the area of sector BOD? Explain.

11 cm 1.7 ft in.23

120!

6 cm 8 ft

6 m

60!

STEM

45!

18 yd16 cm

120!

26 m45!

16 cm

9 cm120! 2 ft

12 m60!

14 in.

STEM8 mm

2 mm

4 mm

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472 Lesson 11-3 Areas of Circles and Sectors