1. 12.6 Surface Area & Volume of Spheres

2. Definitions
Sphere – the locus of points in space that are a given distance from a given point. (looks like a ball)
Center of a Sphere – the given point in the middle.
Radius of a Sphere – segment from the center to a point on the sphere.
Chord of a Sphere – a segment whose endpoints are on the sphere.
Diameter of a Sphere – a chord that goes through the center.

3. C is the center of the sphere.
Parts of a Sphere
C is the center of the sphere.
AB is a diameter.
CB & AC are radii.
DE & AB are chords. C A B E D

4. Thm 12.11 – Surface Area of a Sphere
S = 4r2
(it takes 4 circles to cover a sphere)
Why isn’t there a lateral area formula?
Because spheres have no bases!
Ex: Find the surface area of a sphere with a diameter of 8 cm.
S = 4(4)2
S = 4(16)
S = 64 cm2

5. More Definitions
Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center.
Hemisphere – ½ of a sphere.
** Every great circle splits a sphere into 2 hemispheres.

6. Ex: The circumference of a great circle of a sphere is 16 m
Ex: The circumference of a great circle of a sphere is 16 m. What is the surface area of the sphere?
S = 4r2
S = 4(8)2
S = 4(64)
S = 256 m2
C = 2r
16 = 2r
16 = 2r
8 m = r

7. Ex: Find the volume of a sphere with a radius of 3 ft.
Thm – Volume of a Sphere
Ex: Find the volume of a sphere with a radius of 3 ft.
V = 36 ft3