NOTE BOOK

In the Real WorldButton Designs You are making a design for a circular button. Your design fits on a circle with a radius of 3 centimeters. How much area will be covered by your design?

Area of a Circle

Words Area = (pi)(radius) 2

Algebra A = π r 2.r

Area of a Circle10 4.

The area of a circle is the amount of surface covered by the circle.

Finding the Area of a CircleEXAMPLE 1To answer the question on the previous slide, let us find the area of a circle with a radius of 3 centimeters. Round to the nearest square centimeter.

A = π r 2 Write the formula for the area of a circle.

Substitute 3.14 for π and 3 for r.

Simplify.

≈ (3.14) (3) 2

= 28.26

ANSWER The area covered by your design is about 28 square centimeters.

Area of a Circle10 4.

Finding the Area of Combined FiguresEXAMPLE 2Basketball Find the area of the free throw area to the nearest square foot.

Find the area of each shape.

= 19 • 12

ANSWER The area of the free throw area is about 285 square feet.

SOLUTION

Rectangle Half-circleA = π r 21

2A = l w

= 56.52

Add the areas together to find the total area.

228 + 56.52 = 284.52

≈ (3.14)(6) 212

= 228

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Area of a Circle10 4.

Comparing AreasEXAMPLE 3Pizza How many times as great as the area of an 8 inch pizza is the area of a 16 inch pizza?

Find the area of each pizza.

≈ (3.14)(4) 2

ANSWER The area of a 16 inch pizza is 4 times the area of an 8 inch pizza.

SOLUTION

8 inch pizza 16 inch pizzaA = π r 2

= 200.96 in. 2

Divide the area of the 16 inch pizza by the area of the 8 inch pizza.

= 4

= 50.24 in. 2

A = π r 2

≈ (3.14)(8) 2

200.9650.24

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Area of a Circle10 4.

Making Circle Graphs

Area of a Circle10 4.

Each sector is formed by an angle whose vertex is the center of the circle.

In a circle graph, the sum of the measures of all these angles is 360º.

A circle graph is made of sectors that represent portions of a data set.

Types of Ski Trails

Fraction of Trails

ExpertIntermediateBeginnerTrail Type

12

15

310

Making a Circle GraphEXAMPLE 4

SOLUTION

Find the angle measure of each sector. Each sector’s angle measure is a fraction of 360º. Multiply each fraction in the table by 360º to get the angle measure for each sector.

Ski Trails The table shows what fraction of the trails at a ski resort are beginner, intermediate, and expert. Make a circle graph to represent the data.

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Area of a Circle10 4.

Intermediate: (360º) = 180º12

Expert: (360º) = 72º15

Beginner: (360º) = 108º310

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Making a Circle GraphEXAMPLE 4

Draw the circle graph.

Use a compass to draw a circle.

Use a protractor to draw the angle for each sector.

Label each sector and give your graph a title.

180º 108º

72º

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Area of a Circle10 4.