How are the parts of a circle related?
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1 Student Handout 1 How are the parts of a circle related? A circle has many specific parts including the Label the parts of the circle below. circumference radius, diameter, and circumference. d r Determine the ratio of the circumference of a circle to its diameter. Diameter Circumference Ratio (y/x) The ratio between the circumference and the diameter is represented by, π which is approximated to. Circumference formulas C = 2πr or C =πd Use the formulas to find the circumference of the circles below. Label the various parts of the circle. Circle 1 Circle 2 Circle 3 6in 14cm 3.5m Formula = Formula = Formula = Plug in #s = Plug in #s = Plug in #s = c = 2πr c = πd c = 2πr c = 2 6 c = 14 c = circumference = circumference = circumference = in cm m
2 The formula for the area of a circle can be derived by splitting the à r circle into smaller segments. 1 2 C 1 2 C r A = A = 1 2 2πr r A = πr² Area is the surface measurement of a two-dimensional. figure Area formula A = πr 2 Use the formula to find the area of the circles below. Circle 1 Circle 2 Circle 3 r = 3in 10cm 6m Formula = πr Formula = Formula = Plug in #s = Plug in #s = Plug in #s = 2 πr² πr² 3 2 5² 6² AREA = AREA = AREA = in² 78.5 cm² m² Describe the difference between the area and the circumference of a circle. The area measures the covering, while the circumference measures the distance around the circle. Summarize today s lesson: Note: This is a strategy for moving information from short-to long-term memory. I usually ask students to write 2-3 sentences.
3 Homework 1 How are the parts of a circle related? Complete the table below by finding the area and the circumference of the circles below. Circle Circumference area formula: 2πr 10in radius = 10 in diameter = 20 in circumference: 62.8 in area: 314 in² formula: 2πr 12ft radius = 6 ft diameter = 12 ft circumference: ft area: ft² formula: 2πr 3m radius = 3 m diameter = 6 m circumference: m area: m² formula: 2πr 18cm radius = 9 cm diameter = 18 cm circumference: cm area: cm²
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5 Student Handout 2 HOW can we solve problems involving circles? When solving real life problems, be sure to determine whether you are solving for the 1. A cell phone tower picks up signals within a 65 mile radius. How many square miles of coverage does the cell phone tower provide? r = 65 miles π = area or the. circumference the number of square miles - area A = πr² 65² 13,266.5 miles² 13,266.5 miles² 2. A Ferris wheel measures 40 meters from the top car to the bottom car. A cart travels one time around the Ferris wheel. How many meters will it travel? π = d = 40m the distance around the ferris wheel - circumference C = 2πr C = πd C = 40 C = m m
6 3. Two different circular fountains are being considered for an outdoor patio. How many more square feet will the larger fountain occupy? 9 ft 16 ft r = 8 ft r = 9 ft the difference between the area of both circles A = πr² A = 8² A = ft² A = πr² A = 9² A = ft² the difference is ft² 16 ft 4. The lines on basketball court form a half circle at the free throw line. Use the picture to the right to determine the length of the paint around the ark. 7.5 ft d = 7.5 ft C 2 = 2πr 2 = 3.75 r = 3.75 ft half of the circumference ft
7 Homework 2 HOW can we solve problems involving circles? Answer the questions below. Sketch a diagram to help. 1. A stadium floor that is in the shape of a circle has a diameter with a length of 50 yards. What is the area of the circle on the stadium floor? 2. A play train travels around a Christmas tree in a circle. The train track measures 6 feet in diameter. What is the distance that the train travels? 1,962.5 yd² ft 3. A large pizza is advertised to have a 14 inch diameter. If a customer orders two large pizzas, how many square inches of pizza will he receive? 4. A flower bed surrounds the base of a tree. It is enclosed by stones to form a circle that measures feet around. What is the radius of the circle? in² 5. A circle has an area of 78.5 square inches. What is the diameter of the circle? 4 ft 6. Ms. Michaels made an apple pie with a radius of 5 inches. She cut the pie into six equal slices. Find the approximate area of each slice. 10 in about 13 in²
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Lesson 8: Applications of Quadratics Quadratic Formula: x = b± b 2 4ac 2a ; Vertex: ( b, f ( b )) 2a 2a Standard: F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand