circumference: the distance around the circle. if you unwrap a circle, how long will the line be?...

CIRCUMFERENCE:The distance around the circle.

If you unwrap a circle, how long will the line be?

C d or 2C rSo what is ?anyway

AREA FORMULA

The area of a circle with radius r

is given by

2A rr

This gives us the

EXACT number of squares!

(It’s usually not a whole

number.)

Fraction of a Circle What fraction of the

whole circle is a given arc?

1. Find the measure of the central angle.

2. Divide by 360, the total number of degrees in the circle.

diameter

180º

180 1

360 2

This arc is one-half of a circle.

Fraction of a Circle What fraction of the whole

circle is this (major) arc?1. Find the measure of the

central angle. The major arc measure is:

360º – minor arc measure

= 360º - 140º= 220º

1. Divide by 360, the total number of degrees in the circle.

This arc is eleven-eighteenths of a circle.

140º

220º

220 11

360 18

Arc Length Formula

Arc Length= (fraction of the circle) X (circumference)

= fr x C

= x 2r = x 2r

central angle

360

a

360

Example: Find the Arc LengthA.L. (arc length)

= fraction *circ.

=

in

aC

36072

2 836016

510.1

in Exact Answer (in terms of )

Approximate Answer (nearest tenth)

SECTORsector of a circle - part of the

interior of a circle bounded by two radii and an arc.

AREA OF A SECTOR

The area of a sector of a circleThe size of a slice of pizza. The FRACTION OF THE CIRCLE

multiplied by the AREA OF THE CIRCLE.

Area of a Sector Formula

Area of a Sector

= (fraction of the circle) X (area of circle)

= fr x A

= X r2

= X r2

central angle

360

a

360

A.S. (area of a sector)= fraction *area

72°

in2

in2

Exact Answer (in terms of )

Approximate Answer (nearest tenth)

Example: Find the Area of the Sector

2

aA

36072

836064

540.2