NOTE BOOK In the Real World Button Designs You are making a design for a circular button. Your design fits on a circle with a radius of 3 centimeters.

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NOTE BOOK In the Real World Button 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 Circle The area of a circle is the amount of surface covered by the circle.

Finding the Area of a Circle EXAMPLE 1 To 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 = ANSWER The area covered by your design is about 28 square centimeters. Area of a Circle 10 4.

Finding the Area of Combined Figures EXAMPLE 2 Basketball Find the area of the free throw area to the nearest square foot. Find the area of each shape. = ANSWER The area of the free throw area is about 285 square feet. SOLUTION RectangleHalf-circle A = π r A = l w = Add the areas together to find the total area = ≈ (3.14)(6) = Area of a Circle 10 4.

Comparing Areas EXAMPLE 3 Pizza 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 pizza A = π r 2 = in. 2 Divide the area of the 16 inch pizza by the area of the 8 inch pizza. = 4 = in. 2 A = π r 2 ≈ (3.14)(8) Area of a Circle 10 4.

Making Circle Graphs Area of a Circle 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 Making a Circle Graph EXAMPLE 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. 1 Area of a Circle Intermediate: (360º) = 180º 1212 Expert: (360º) = 72º 1515 Beginner: (360º) = 108º 3 10

. Making a Circle Graph EXAMPLE 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 2 Area of a Circle 10 4.