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GEOMETRY 3A CHAPTER 10 POWERPOINT PRESENTATION. CIRCLES AND SPHERES. LEARNING TARGETS. AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: IDENTIFY FORMULAS FOR: CIRCUMFERENCE, DIAMETER, RADIUS SOLVE PROBABILITY PROBLEMS DETERMINE THE AREA OF A CIRCLE

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Presentation Transcript
learning targets
LEARNING TARGETS
  • AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:
  • IDENTIFY FORMULAS FOR: CIRCUMFERENCE, DIAMETER, RADIUS
  • SOLVE PROBABILITY PROBLEMS
  • DETERMINE THE AREA OF A CIRCLE
  • DEFINE TRIGONOMETRIC RATIOS AND USE THEM
  • DETERMINE VOLUME AND SURFACE AREA OF A SPHERE
circle vocabulary
CIRCLE - VOCABULARY
  • CIRCLE: SET OF POINTS AT THE SAME DISTANCE FROM A GIVEN POINT
  • RADIUS: (r) DISTANCE BETWEEN THE CENTER OF A CIRCLE AND ANY POINT ON THE CIRCLE
  • CHORD: LINE SEGMENT JOINING TWO POINTS ON A CIRCLE
  • DIAMETER: (d) A CHORD THAT PASSES THROUGH THE CENTER OF A CIRCLE
  • CIRCUMFERENCE: (c)THE COMPLETE LENGTH AROUND A CIRCLE
  • QUADRANT: ONE-FOURTH OF A CIRCLE
the ratio pi
THE RATIO PI
  • Pi = 22/7 or 3.14
  • Its symbol is:
circumference
Circumference
  • Circumference of a circle:
estimation of area of circle
Estimation of Area of Circle
  • Area estimation formula: area of a circle = 3r²
  • Where r = radius
  • Approximating the area of a circle:
area and probability
Area and Probability
  • Probability means the chances or likelihood of an event happening.
  • Suppose you pick any point inside the circle, what is the probability of picking a point in the top semi-circle? 1 out of 2
  • If a circle is split into four quadrants, what is the probability of landing on a quadrant with an even number: 1 out of 2
area of a circle
Area of a Circle
  • Area = πr² (use when you know the radius)
  • Area = ¼πd² (use when you know the diameter)
additional circle vocabulary
ADDITIONAL CIRCLE VOCABULARY

SECTOR: THE AREA ENCLOSED WITHIN A CENTRAL ANGLE OF A CIRCLE

CENTRAL ANGLE: AN ANGLE WITH ITS VERTEX AT THE CENTER OF A CIRCLE AND THE CIRCLE’S RADII (PLURAL OF RADIUS) AS ITS SIDE

ARC: A PORTION OF A CIRLCE BOUNDED BY TWO DISTINCT POINTS ON THE CIRCLE

more circle vocabulary
More Circle Vocabulary
  • Inscribed Angle: An angle formed by two chords that intersect on the circle.
  • Intercepted Arc: The arc of a circle within an inscribed angle.
  • Tangent: A line that touches but does not intersect a circle.
  • Point of Tangency: The point where the tangent touches the circle
cirlce vocabulary continues
CIRLCE VOCABULARY, CONTINUES…
  • Perpendicular Bisector: A set of points equidistant from two given points.
  • Equidistant: At an equal distance.
  • Locus of Points: A set of points that satisfy a certain condition.
and the circle vocabulary just keeps coming
And the Circle Vocabulary Just Keeps Coming!!!!
  • Circumcircle: A circle that passes through three vertices of a triangle.
  • Circumcenter: Center of a circumcircle and located at the intersection of the perpendicular bisectors of any two sides of a triangle.
  • Angle Bisector: Locus of points equidistant from the sides of an angle.
  • Incircle: A circle inside a triangle and tangent to each of the triangle’s sides.
what that looks like1
What That Looks Like!
  • Circumcircle & Circumcenter:
sine cosine tangent
Sine, Cosine, Tangent
  • Unit Circle: Circle whose radius is one.
  • Sine (sin): for an angle of a right triangle, not the right angle, the ratio of the length of the opposite leg divided by the length of the hypotenuse.
  • Cosine (cos): for an angle of a right triangle, not the right angle, the ratio of the length of the adjacent leg divided by the length of the hypotenuse.
  • Tangent (tan): for an angle of a right triangle, not the right angle, the ratio of the length of the opposite side divided by the length of the adjacent leg.
trigonometry
Trigonometry
  • Trigonometry – The branch of mathematics dealing with the relation between the sides and angles of triangles. For right triangles.
the sphere
The Sphere
  • Sphere: Locus of points in space equidistant from a fixed point.
  • Great Circle: Circle on a sphere whose center is the center of the sphere and whose radius equals the radius of the sphere.
  • Hemisphere: Half of a sphere.
  • Poles: Endpoints of the diameter of a sphere.
  • Formulas: SA = 4πr² Volume: 4/3πr³