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Geometry 1 Area and Circumference of a Circle

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Page 1: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Geometry

1

Area and Circumference

of a Circle

Page 2: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Central AngleA central angle is an angle whose vertex is at the center of the circle.

2

The measure of a minor arc is the measure of its central angle.

The measure of a major arc is 360 minus the measure of its central angle.

The arc measure is written as

Central Angle

A

B

CBAC

Page 3: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Circumference Example:

2 (3)CExample: Find the circumference of the following circle.

3 cm6C

18.85C cm

• When finding the circumference of a circle, you can leave your answer in terms of pi.

Page 4: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Circumference:

Circumference is the distance around the circle.

2C r

2 (3)C

4

C d2d r

Formula: Or

Example: Find the circumference of the following circle.

3 cm6C

18.85C cm

where

Page 5: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Example: If a bicycle tire has a diameter of 26 inches, how far does it travel in 1000 revolutions of the tire? Use 3.14.

Example: The rim of a satellite dish has a diameter of 7 feet. Find the circumference of the rim and the area of the circle defined by the rim. Use 3.14.

Page 6: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Example: A Ferris wheel has diameter of 42 feet. How far will a rider travel during a 4 minute ride if the wheel rotates once every 20 seconds? Use 22/7.

Example: The tires of a racing bike are approximately 70 cm in diameter. How far does a bike racer travel in 5 minutes if the wheels are turning at a speed of 3 revolutions per second? How many revolutions does a wheel make in 22 km race? Use 22/7.

Page 7: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Area of a Circle

Area of a circle is the number of unit squares that can fit into a circle.

2(3)A 9A

7

2A r

Example: Find the area of the following circle.

3 cm

228.27A cm

Formula:

Page 8: Geometry 1 Area and Circumference of a Circle. Central Angle A central angle is an angle whose vertex is at the center of the circle. 2 The measure of

Complete the table below and leave your answers in terms of pi.

Radius 8

Diameter

Circumference 26π

Area 18π

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Inscribed Angle A measures _____ Arc BC measures _____ Central Angle measures _____

Inner Circle of Central Iowa

Congruence line,angle,triangles,rectangle-circle etc

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GEOMETRY R Unit 13 Circles - Revizecms5.revize.com/revize/williamsvilleschools... · circle enclosed by 2 radii and the edge of the circle. A central angle of a sector is an angle

ARC LENGTH AND SECTOR AREA - dangmath.com · A. Sector is a region of the circle that bounded by two radii and an arc of a circle B. The Central Angle of a sector is the angle formed

Angle Properties of the Circle

Aim: How do we graph data on a circle graph? A central angle has the center of a circle for its vertex the rays are radii of the circle A circle graph

Web viewarc, arc length, central angle, chord, diameter, minor arc, major arc, arc measure, inscribed angle, circumscribed circle, inscribed circle, cyclic quadrilateral, secant, secant

Home - Warren County Public Schools · 12-2 Chords and Arcs central angle - an angle whose vertex is the center of the circle note Theorem 12-4 and Its Converse Theorem Within a circle

1. Circle A has a center at (-1, -1), and circle B has a ...teachers.dadeschools.net/rvancol/GeometryEOC/FSAEOCGeometryPr… · 4. Circle Q has a radius r with a central angle ∠AQB

circletheorems - Instant Display Teaching Resources · circle from the same points, . CIRCLE THEOREM 2 The angle in a semi-circle is 900, This is a special case of theorem The angle

November 19, 2009. A central angle of a circle is an angle with its vertex at the center of the circle. The figurebelow illustrates

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