Section 7 –7 Areas of Circles & SEctors

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Presentation transcript:

Section 7 –7 Areas of Circles & SEctors Objectives: To find the areas of circles, sectors, and segments of circles

Area of a Circle 𝑨=𝝅 𝒓 𝟐

Example 1 Real-World Connection A) How much more pizza is in a 12-inch diameter pizza than in a 10-inch pizza?

How much more pizza is in a 14-inch pizza than in a 12-inch pizza?

C). A circular archery target has a 2 ft. diameter C) A circular archery target has a 2 ft. diameter. It is yellow except for a red bull’s eye at the center with a 6 in. diameter. Find the area of the yellow region. Round to the nearest whole number.

Sector of a Circle: A region bounded by an arc of the circle and two radii to the arc’s endpoints. When naming a sector, you use the arc’s two endpoints and the center of the circle.

Area of a Sector of a Circle

Example 2 Finding the Area of a Sector of a Circle A) Find the area of sector ZOM. Leave your answer in terms of π.

Find the area of sector ACB. Leave your answer in terms of π.

C). A circle has a diameter or 20 cm C) A circle has a diameter or 20 cm. What is the area of a sector bounded by a 208° major arc? Round your answer to the nearest tenth.

D) Find the area of the shaded region. Leave your answer in terms of π.

Homework Textbook Page 397 – 398; #2 – 16 Even

Segment of a Circle: A part of a circle bounded by an arc and the segment joining its endpoints.

Area of a Segment

Example 3 Finding the Area of a Segment of a Circle A) Find the area of the shaded segment. Round your answers to the nearest tenth.

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

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

D). A circle has a radius of 12 cm D) A circle has a radius of 12 cm. Find the area of the smaller segment of the circle determined by a 60° arc. Round your answer to the nearest tenth.