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Geometry of Circles: Diameter, Radius, Circumference, and Area

Learn about the standard notation, properties, and formulas in geometry related to circles, including diameter, radius, circumference, and area. Explore examples and calculations to deepen your understanding.

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Geometry of Circles: Diameter, Radius, Circumference, and Area

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  1. Chapter 9 Geometry

  2. 9 Geometry

  3. 1.1 Standard Notation Slide 3 9.3 Circles

  4. B C r O d A Segment is a diameter. A diameter is a segment that passes through the center of the circle and has endpoints on the circle. Segment is called a radius. A radius is a segment with one endpoint on the center and the other endpoint on the circle.

  5. Diameter and Radius Suppose that d is the diameter of a circle and r is the radius. Then d = 2  r and

  6. Example • Find the length of a radius of this circle. • Solution 16 m The radius is 8 m.

  7. Example • Find the length of a diameter of this circle. • Solution ½ ft The diameter is 1 ft.

  8. The perimeter of a circle is called its circumference. Circumference and Diameter The circumference C of a circle of diameter d is given by The number is about 3.14, or about

  9. Example • Find the circumference of this circle. Use 3.14 for . • Solution 8 m

  10. Circumference and Radius The circumference C of a circle of radius r is given by

  11. Example • Find the circumference of this circle. Use 22/7 for . • Solution 140 in.

  12. 5.2 km 5.6 km 8.2 km Example • Find the perimeter of this figure. Use 3.14 for . • Solution • We let P = the perimeter. • Since there is 1/2 a circle replacing the fourth side of a square, we add half the circumference to the lengths of the three line segments.

  13. Area of a Circle The area of a circle with radius of length r is given by r

  14. Example • Find the area of this circle. Use 3.14 for . Round to the nearest hundredth. • Solution 3.6 m

  15. Example • A local pizza parlor is ordering new square serving plates. If they order a 16 in. plate how much area will show when a 14 in. diameter pizza is placed on the pan? • Familiarize. Look at the drawing, notice • that the corners of the box will be visible when the pizza is in place. We let A = the area of the box visible. 14 in.

  16. continued • Translate. • Area of box minus Area of pizza is Visible Area • s s –   r  r = A • Solve. The radius is ½ the diameter, or 7 in. • s s –   r  r = A • 16 in.  16 in. – 3.14  7 in.  7 in.  A • 256 in2 – 153.86 in2  A • 102.14 in2  A

  17. continued • Check. We can check by repeating our calculations. Note also that the area of the plate does not exceed the area of the pizza. • State. • When the pizza is in place, about 102.14 in2 of plate will be visible.

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