#### Transcript of Arc Lengths and Area of Sector

**Circles**

**Arc Length and Area of Sector**

Things to Know

Few things that we need to know and understand:

Radius

Circumference

Area

Central Angle

What kind of relationships do these concepts have that will help us solve for the Arc Length and the area of a Sector?

Radius

Definition:

The distance from the center of a circle to a point on the circle.

Area

Definition:

The number of square units it takes to exactly fill the interior of a circle.

Formula:

Area=πr^2 (r is the radius)

Area= C^2/4π (C is the circumference)

Central Angle

Definition:

The angle at the center of a circle by two given points on the circle.

Circumference

Definition:

The distance around the edge of a circle, also known as perimeter of the circle.

Formula:

Circumference=2πr (r is the radius)

Arc Length

Area of a Sector

Examples

1. What is the arc length if the radius of the circle is 7cm and its central angle is 30 degrees?

2. What is the area of the sector if the radius of the circle is 4 cm and its central angle is 45 degrees?

Solutions

1. C=2πr=2π(7)=14π

a/14π=30/360

360a=1,319.469

a=1,319.47/360=3.665

so the arc lenth is 3.655cm.

2. A=πr^2=π(4)^2=16π

s/16π=45/360

360s=2,261.947

s=6.283

so the area of the sector is 6.283cm.

Importance to Society and Daily Life

Circle is one of the fundamental figures in our universe. Everywhere we go, we can see circles. Learning about arc lengths and area of sectors is very important to our daily lives because arc lengths and sectors tells us how to build freeways, build roller costers, which areas we should grow our crops on, etc. Below is a short clip of how sectors can be used from crops.

With a partner, come up with two other examples where arc lengths or sectors are used in our daily lives. Do you think that arc length and sectors are important now?

What do you think is the relationship between the circumference and the radius is?

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