This document provides information about circles and spheres. It defines circles as 2D shapes with all points equidistant from the center. It describes circle components like radius, diameter, circumference, arcs, and sectors. Formulas are given for circumference as 2πr or πd, arc length as rθ, sector area as 1/2r2θ, and segment area as sector area minus triangle area. The document also defines spheres as 3D shapes that are circular surfaces. Formulas given for sphere surface area as 4πr2 and volume as (4/3)πr3. Examples are provided for using the circumference, arc length, sector area, and surface area/volume formulas.

1. CIRCLE

2. Introduction
-2-dimension
-Circular geometry shape
- Set of all point in the
plane
A circle is…

3. Constructing a Circle
Compass is use to create a
Perfect Circle with accurate
measurements
-To make sure the r (radius) and
the d (diameter) are the same at
all points

4. Circle
Arc-A closed segment of a
curve
Sector-A region of a circle
which is "cut off" from the
circle by a chord
Segment-A portion of a disk
enclosed by two radii and an
arc

5. Circle
Radius-A distance from the
center of the circle to any
point of the circumference
Diameter-A distance between
two point passing through the
center
Circumference-Linear
distance around the edge of a
closed curve

6. Piiiiiiii…
Do You Know…
Pi is a irrational number
since its value is not
proportion
Pi has 18 digit decimal
place
-which is
3.141592653589793238

7. Circumference
In which π=22/7 or
3.142
-C=2πr or πd

8. Circumference
Example: You walk around a circle which has a diameter of
100m, how far have you walked?
Distance walked = Circumference = π × 100m
= 314m (to the nearest m)
-Using the formula of πd

9. Arc Length
s=arc length of the circle
r=radius
0=degree/radian (converted)
Arc, s=r0

10. Arc Length
s=r0
s=9(1.05 rad)
s=9.424 cm
Example:

11. Area of the Sector
s=sector of the circle
r=radius
0=degree/radian

12. Area of the Sector
s=1/2r2 0
s=1/2(24) 2
(2.095 rad)
s=603.072 cm2
Example:

13. Area of the Segment
Area of Segment=Area of sector-Area of
triangle
r2(0-sin 0)
r=radius
0=degree/radian

14. Area of the Segment
s=1/2r2 (0-sin 0)
s=1/2(7) 2 (1.746
rad)-sin (1.746 rad)
s=42.01 cm2
Example:

15. SPHERE

16. Introduction
A sphere is…
-3 Dimension
-Circular in shape
-Rounded ball surface
completely

17. Surface Area
A=4πr2
A=Surface area
r =Radius

18. Surface Area
A=4πr
A=4(22/7)(5) 2
A=314.29cm2

19. Volume
V= πr3
V=Volume
r=radius

20. Volume
V=4/3 (22/7)(8)3
V=2145.52cm3