ACTIVITY: Estimating the Area of a Circle
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1 8. Areas of Circles How can you find the area of a circle? ACTIVITY: Estimating the Area of a Circle Work with a partner. Each square in the grid is unit by unit. a. Find the area of the large 0-by-0 square. b. Copy and complete the table. Region Area (square units) c. Use your results to estimate the area of the circle. Explain your reasoning. Geometry In this lesson, you will find areas of circles and semicircles. d. Fill in the blanks. Explain your reasoning. Area of large square = 5 square units Area of circle 5 square units e. What dimension of the circle does 5 represent? What can you conclude? Chapter 8 Circles and Area
2 ACTIVITY: Approximating the Area of a Circle Work with a partner. a. Draw a circle. Label the radius as r. b. Divide the circle into 4 equal sections. r Math Practice Interpret a Solution What does the area of the parallelogram represent? Explain. c. Cut the sections apart. Then arrange them to approximate a parallelogram. d. What is the approximate height and base of the parallelogram? e. Find the area of the parallelogram. What can you conclude?. IN YOUR OWN WORDS How can you find the area of a circle? 4. Write a formula for the area of a circle with radius r. Find an object that is circular. Use your formula to find the area. Use what you learned about areas of circles to complete Exercises 5 on page 6. Section 8. Areas of Circles
3 8. Lesson Lesson Tutorials Area of a Circle Words The area A of a circle is the product of π and the square of the radius. Algebra A = π r EXAMPLE cm Finding Areas of Circles a. Find the area of the circle. Use for π. Estimate 50 = 50 A = π r Write formula for area. Substitute for π and for r. = 49 Evaluate. Divide out the common factor. = 54 Multiply. The area is about 54 square centimeters. Reasonable? in. b. Find the area of the circle. Use.4 for π. The radius is 6 = inches. Estimate 0 = 50 A = π r Write formula for area..4 Substitute.4 for π and for r. =.4 69 Evaluate. = Multiply. The area is about square inches. Reasonable? Exercises 0. Find the area of a circle with a radius of 6 feet. Use.4 for π.. Find the area of a circle with a diameter of 8 meters. Use for π. 4 Chapter 8 Circles and Area
4 EXAMPLE Describing a Distance You want to find the distance the monster truck travels when the tires make one 60-degree rotation. Which best describes this distance? A the radius of the tire B the diameter of the tire C the circumference of the tire D the area of the tire The distance the truck travels after one rotation is the same as the distance around the tire. So, the circumference of the tire best describes the distance in one rotation. The correct answer is C.. You want to find the height of one of the tires. Which measurement would best describe the height? EXAMPLE Finding the Area of a Semicircle stage 0 ft orchestra pit Find the area of the semicircular orchestra pit. The area of the orchestra pit is one-half the area of a circle with a diameter of 0 feet. The radius of the circle is 0 = 5 feet. A = π r Divide the area by..4 5 =.4 5 Substitute.4 for π and 5 for r. Evaluate 5. = 5.5 Simplify. So, the area of the orchestra pit is about 5.5 square feet. Exercises 5 Find the area of the semicircle yd 6. cm 8 m Section 8. Areas of Circles 5
5 8. Exercises Help with Homework. VOCABULARY Explain how to find the area of a circle given its diameter.. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. with a diameter of m? with a diameter of 00 cm? with a radius of 00 cm? with a radius of 500 mm? 9+(-6)= +(-)= 4+(-9)= 9+(-)= Find the area of the circle. Use.4 or for π mm 4 cm 5. 0 in in. cm.5 ft 9. Find the area of a circle with a diameter of 56 millimeters. 0. Find the area of a circle with a radius of 5 feet.. TORTILLA The diameter of a flour tortilla is inches. What is the area?. LIGHTHOUSE The Hillsboro Inlet Lighthouse lights up how much more area than the Jupiter Inlet Lighthouse? Jupiter Inlet Lighthouse PALM BEACH Hillsboro Inlet Lighthouse BROWARD 8 mi 8 mi 6 Chapter 8 Circles and Area
6 Find the area of the semicircle in in. 40 cm ft 6. REPEATED REASONING Consider five circles with radii of,, 4, 8, and 6 inches. Radius Circumference Area π in. π in. a. Copy and complete the table. Write your answers in terms of π. b. Compare the areas and circumferences. What happens to the circumference of a circle when you double the radius? What happens to the area? c. What happens when you triple the radius?. DOG A dog is leashed to the corner of a house. How much running area does the dog have? Explain how you found your answer. 8. CRITICAL THINKING Is the area of a semicircle with a diameter of x greater than, less than, or equal to the area of a circle with 0 ft a diameter of x? Explain. Find the area of the shaded region. Explain how you found your answer ft 9m 5 in. 4 ft 9m Evaluate the expression. (Skills Review Handbook). ()(4) + 6(5) () 5 5. MULTIPLE CHOICE What is the product of 8 and? A 8 B 4 5 (Section.4) C 4 5 Section 8. ms_red pe_080.indd 4. (6) + D 8 Areas of Circles //5 8:54:4 AM
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Think of three math problems using the four operations where order matters and three where order doesn t matter. ACTIVITY: Commutative Properties
3.3 Properties of Addition and Multiplication operation matter? Does the order in which you perform an ACTIVITY: Does Order Matter? Work with a partner. Place each statement in the correct oval. a. Fasten
A circle is the set of points that are equidistant from a special point in the called the.
NAME Module 9 Lesson 3 Characteristics of Geometric Shapes Lesson Notes 9.3 Lesson Objectives Model and identify circle, radius, diameter, center, circumference, and chord. Draw, label, and determine relationships
Lesson 3-7: Absolute Value Equations Name:
Lesson 3-7: Absolute Value Equations Name: In this activity, we will learn to solve absolute value equations. An absolute value equation is any equation that contains an absolute value symbol. To start,
Chapter 1 Homework Problems
Chapter 1 Homework Problems Lesson 1.1.1 1-4. Angelica is working with function machines. She has the two machines shown at right. She wants to put them in order so that the output of the first machine
Essential Question How can you solve an absolute value inequality? Work with a partner. Consider the absolute value inequality x
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Lesson 4.1 (Part 1): Roots & Pythagorean Theorem
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