Download presentation

Presentation is loading. Please wait.

1
**MATH 3A CHAPTER 10 POWERPOINT PRESENTATION**

CIRCLES AND SPHERES

2
**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

3
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

4
WHAT THAT LOOKS LIKE

5
CHORDS

6
THE RATIO PI Pi = 22/7 or 3.14 Its symbol is:

7
Circle Formulas Area:

8
Circumference Circumference of a circle:

9
**2 formulas (if you know the radius or the diameter)**

10
**Estimation of Area of Circle**

Area estimation formula: area of a circle = 3r² Where r = radius Approximating the area of a circle:

11
**Symbol for approximately:**

12
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

13
**Area = πr² (use when you know the radius) **

Area of a Circle Area = πr² (use when you know the radius) Area = ¼πd² (use when you know the diameter)

14
**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

15
**WHAT DOES THAT LOOK LIKE?**

16
**Sector/Segment/Quadrant**

17
Central Angles

18
ARCS

19
**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

20
**Tangent & Point of Tangency**

21
**Inscribed Angle & Intercepted Arc**

22
**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.

23
**Perpendicular Bisector**

24
Equidistant Points

25
Locus of Points

26
**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.

27
What That Looks Like! Circumcircle & Circumcenter:

28
Angle Bisectors

29
Incircle

30
**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.

31
Trigonometry Trigonometry – The branch of mathematics dealing with the relation between the sides and angles of triangles. For right triangles.

32
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

33
**What the Parts of a Sphere Look Like**

Great Circle:

34
Hemispheres

35
Poles

Similar presentations

Presentation is loading. Please wait....

OK

Circles Chapter 10.

Circles Chapter 10.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on memory management in os Ppt on series and parallel circuits worksheet Ppt on power line communications Ppt on founder of facebook Download ppt on rotation and revolution of earth Ppt on area of trapezium math Ppt on simultaneous ac-dc power transmission Ppt on seasons in french Ppt on non agricultural activities done Ppt on care of public property record