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Circles: Radius, Diameter, Circumference & Area. During this lesson, you will: Define circles & their parts Solve problems involving the circumference/diameter ratio Solve problems involving the area of circles. B with radius AB. Part I: Defining Circles & Their Parts.
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Circles: Radius, Diameter, Circumference & Area During this lesson, you will: Define circles & their parts Solve problems involving the circumference/diameter ratio Solve problems involving the area of circles Geometry
B with radius AB Part I: Defining Circles & Their Parts Circles are named by their centers. The circle below is B. circle A is the set of all points in a plane at a given distance from a given point. The given point is the ______ of the circle. center center radius A B radius The given distance is the ______ of the circle. A segment form a point of the circle to the center is also called a ______. radius Geometry
Note: D = 2r; r = ½ D Defining Circles & Their Parts In a polygon, the “distance around the figure” is called the ________. In circles, this distance is the___________. The segment which intersects the circle’s center is called the ________. perimeter circumference diameter Geometry
Part II: The Circumference/Diameter Ratio Mark two quarters with a pencil or felt-tip pen. Now, with one quarter remaining motionless, rotate the second quarter around it, being sure that it never slips, but is always tangent to it. How many turns has it made around its center? Since the circumferences of the two circumferences are the same, one coin will rotate in _____ revolution (s). Geometry
The Circumference/Diameter Ratio There is a special relationship which exists between the circumference and diameter of every circle. If you divide the circumference of an object by its diameter, you get a number slightly greater than 3. The more accurate your measurements, the closer the ratio will be equal to ___. π is an approximation for 3.14 or 22/7. π Geometry
Circumference Theorem If C is the circumference and D is the diameter of a circle, then there is a number π such that C = _____. Since D = _____where r is the radius, then C = _______. Π D 2 r 2Π r Geometry
EXAMPLE A If a circle has a circumference of 12 π meters, what is the radius? C = 2 Π r 12 Π m = 2 Π r 6 m 6 12 Π m = 2 Π r 2 Π 2 Π 1 Geometry
EXAMPLE B If a circle has a diameter of 3 meters, what is the circumference? Note: Only use 3.14 or 22/7 for Π when directed to do so. C = Π D C = Π (3m) C = 3Πm Geometry
Final Checks for Understanding Orally set up statement problems on Circumference Theorem WS. Be prepared to explain how you decided which of the two formulas for circumference, C = πD or C = 2πr, to use. Note: D = 2r; r = ½ D Geometry
Homework Assignment Circumference/Diameter Ratio WS, plus Mental Math Chart Geometry
During this lesson, you will solve problems involving areas of circles. Part III: Area of Circles Geometry
Circle Area Theorem The area of a circle is given by the formula, Ao = ______, where A is the area and r is the radius of the circle. Π r 2 Geometry
A circle's area is found using the formula: A = Π r 2 But where does this formula come from?Let's find out ... Geometry
EXAMPLE A Ans:28.3 in. 2 If a circle has a diameter of 6 inches, what is the area accurate to the nearest tenth of an inch? Use 3.14 for π. A = Π r 2 Geometry
EXAMPLE B Ans: 12 m If a circle has an area of 144 π m2,what is the radius? A = Π r 2 Geometry
