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Spheres

Lesson : Spheres 2

Spheres

A sphere is formed by revolving a circle about its diameter.

In space, the set of all points that are a given distance from a given point, called the center.

Definition:

Lesson : Spheres 3

Spheres – special segments & lines

Radius: A segment whose endpoints are the center of the sphere and a point on the sphere.

Chord: A segment whose endpoints are on the sphere.

Diameter: A chord that contains the sphere’s center.

Tangent: A line that intersects the sphere in exactly one point.

Radius

Chord

Diameter

Tangent

Lesson : Spheres 4

Surface Area & Volume of Sphere

34

3rVolume (V) =

Surface Area (TA) = 4 π r2

r

Example: Find the surface area and volume of the sphere.

12 cm

2 2

3 3

. 4 12 576

412 2304

3

T A cm

V cm

Lesson : Spheres 5

Great Circle & Hemisphere

Great Circle: For a given sphere, the intersection of the sphere and a plane that contains the center of the sphere.

Hemisphere: One of the two parts into which a great circle separates a given sphere.

Great Circle

Hemisphere

Lesson : Spheres 6

Surface Area & Volume of Hemisphere

Find the surface area and volume of the following solid (Hemisphere).

10 cm2

2

3

3

. 4 10 400

400. 200

24

10 1333.33

1333.3666.7

2

T A of Sphere

T A of Hemisphere cm

V of Sphere

V of Hemisphere cm