Download
8 7 circumference and area of circles n.
Skip this Video
Loading SlideShow in 5 Seconds..
8.7 Circumference and Area of Circles PowerPoint Presentation
Download Presentation
8.7 Circumference and Area of Circles

8.7 Circumference and Area of Circles

147 Views Download Presentation
Download Presentation

8.7 Circumference and Area of Circles

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. 8.7 Circumference and Area of Circles

  2. Definition • A circle is the set of all points in a plane that are the same distance from a given point, called the center of the circle. • A circle with center is called “circle ,” or .

  3. Terms • The distance from the center to a point on the circle is the radius. • The distance across the circle, through the center, is the diameter. • The circumference of a circle is the distance around the circle.

  4. r d Terms • radius • diameter • circumference c

  5. Terms • For any circle, the ratio of the circumference to its diameter is denoted by the Greek letter π, or pi. • The number π is 3.14159…, which is an irrational number, which neither terminates nor repeats. • An approximation of 3.14 is used for π.

  6. Circumference of a Circle • Words • Circumference = π (diameter) = 2π (radius) • Symbols • C = πd or C = 2πr

  7. 4 in. Finding Circumference • Find the circumference of the circle. C = πd or C = 2πr C = 2πr = 2π(4) = 8π = 8(3.14) = 25.12 in.

  8. Area of a Circle • Words • Area = π (radius)2 • Symbols • A = πr2

  9. 7 cm Finding Area of a Circle • Find the Area of the Circle A = πr2 A = π(7)2 A = π(49) A = (3.14)(49) A = 153.94 cm2

  10. r Using the Area of a Circle Find the radius of a circle with an area of 380 square feet. A = πr2 380 = πr2 380/ π = r² 120.96 ≈ r² 11 ft ≈ r

  11. ө Central Angles An angle whose vertex is the center of a circle is a central angle of the circle. A region of a circle determined by two radii and a part of the circle is called a sector of the circle. r

  12. Measurecentral angle Areasector = Areacircle Measurecircle Central Angles Because a sector is a portion of a circle, the following proportion can be used to find the area of a sector. r ө