8-2 FORMULASArea

CircumferenceSectors

REVIEW: RADIUS AND DIAMETERThe RADIUS is the measure of any radius. Radius is usually abbreviated as .

The DIAMETER is the measure of any diameter.

Diameter is usually abbreviated as .

2d r

r

d

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?

3 cmB C

A

(2)( )(3)C 6C 18.8C

2C r

Example: Find the Circumference of the Circle

cmcm

Exact Answer

Approximate Answer

AREAThe area of a region is the number of unit

squares that can fit into the region (or the space inside the region.)

The area of a unit square = length X width= (1 cm) X (1 cm)= 1X1 X cm x cm= 1 cm2

UnitSquareFor area the

units are always

squared!

AREAThe area of a circle is the number

of unit squares that can fit into the circle.

How many squares are in

the circle?You can estimate by counting…

Or use the

formula!

AREA FORMULAThe area of a circle with radius r

is given by

2A rrThis gives

us the EXACT

number of squares!

(It’s usually not a whole

number.)

Find the area of the following circle.

2(3)A 9A 28.27A

cm2

cm2

Approximate Answer

Exact Answer

Example: Find the Area of the Circle

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 1360 2

This arc is one-half of a circle.

Fraction of a Circle What fraction of the

whole circle is this arc?

1. Find the measure of the central angle.

2. Divide by 360, the total number of degrees in the circle. 72 1

360 5

This arc is one-fifth 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 11360 18

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.

central angle a360 360

Fraction of the circle =

a

Arc LengthThe distance around an arc

The amount of crust on a slice of pizza.

The ratio of the center angle and 360° (the FRACTION OF THE CIRCLE) multiplied by the CIRCUMFERENCE

Arc Length FormulaArc Length

= (fraction of the circle) X (circumference)= fr x C

= x 2r

= x 2r

central angle360

a360

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

= fraction *circ. =

in

a C360

72 2 8360165

10.1

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 SECTORThe 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 FormulaArea of a Sector

= (fraction of the circle) X (area of circle)= fr x A

= X r2

= X r2

central angle360

a360

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

a A360

72 8360645

40.2