Chapter 10: Area 10.7 Areas of Circles & Sectors.

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Presentation transcript:

Chapter 10: Area 10.7 Areas of Circles & Sectors

Theorem Area of a Circle – The area of a circle is the product of π and the square of the radius.

Example 1 How much more pizza is in a 12-inch diameter pizze than in a 10-inch pizza?

Sector of a Circle Region bounded by an arc of the circle and the two radii to the arc’s endpoints Named using one endpoint of the arc, the center of the circle, and the other endpoint of the arc Area of a sector is a fractional part of the circle

Theorem Area of a Sector of a Circle – The area of a sector of a circle is the product of the ratio (measure of the arc/360) and the area of the circle.

Example 2 Find the area of sector ZOM. Leave your answer in terms of π.

Example 2a A circle has a diameter of 20 cm. What is the area of a sector bounded by a 208° major arc? Round your answer to the nearest tenth.

Segment of a Circle

Example 3 Find the area of the shaded segment. Round your answer to the nearest tenth.

Example 3a 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.

Homework P , 4, 10, 12, 18, 24, 26, 35