Chapter 1212.6

Surface Area and Volume of Spheres

Definition of a Sphere• The locus of all points in space that are a given

distance from a point • That point is called the center of the sphere• The Radius of the sphere is a segment from the

center to a point on the sphere.• A Chord of the sphere is a segment with

endpoints on the sphere• The Diameter of a sphere is a chord that contains

the center of the sphere

Examples

RadiusDiameter

Chord

Center

Spheres VS Circles

Sphere• Has a center• Has a diameter• Has chords• Contained in space

Circle• Has a center• Has a diameter• Has chords• Lies in a plane

More about circles

• When a plane intersects a sphere the intersection is a– Circle or a Point

• Great Circle– A circle that cuts the sphere into two congruent halves called

hemispheres and contains the center of the sphere

Theorem 12.11: Surface Area of a Sphere

S = 4r2

• S is the surface area

• r is the radius of the sphere

Theorem 12.12: Volume of a Sphere

• V is the volume of the sphere • r is the radius of the sphere

3

3

4rV

Find the Surface area and volume of the sphere

Surface Area

1. S = 4r2

2. Find r:2

3r

3. Fill in formula

94

94

2

34

2

S

Volume

1. 2

3

4rV

2. Find r:2

3r

3. Fill in formula

2

9

8

27

3

4

2

3

3

43

V

Find the Surface area and volume of the sphere

Surface Area

1. S = 4r2

2. Find r: 5r

3. Fill in formula

10025454 2 S

Volume

1. 2

3

4rV

2. Find r: 5r

3. Fill in formula

3

500125

3

45

3

4 3 V

Find the Surface area and volume of the sphere

Surface Area

1. S = 4r2

2. Find r: 8.2r

3. Fill in formula

84.796.144.14 2 S

Volume

1. 2

3

4rV

2. Find r: 8.2r

3. Fill in formula

66.3744.23

44.1

3

4 3 V

Fill in the chart

20 4003

4000

Radius of Sphere

Circumference of Great Circle

Surface area of sphere

Volume of Sphere

10 mm

36

2304

500 /3

18 1296 7776

24 48 18432

5 10 100

Find the surface area of the following figure

1. Area of the cylinder less the top base plus the area of the hemisphere

• )4(2

12 22 rrhrS

144))4(4(2

1)12)(4(2)4( 22 S

Area of Cylinder less the top base

Half the area of the sphere

Find the volume of the following figure

1. Volume of the cylinder less the volume of the hemisphere

• )3

4(

2

1 32 rhrS

3

704))4(

3

4(

2

1)12()4( 32 S

Volume of Cylinder

Half the volume of the sphere

Homework #74Pg 762-764 10-17, 20-29, 35-40