Transcript 12.6 Surface Area & Volume of Spheres

12.6 Surface Area & Volume
of Spheres
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.
Parts of a Sphere
C
A
B
E
D
C is the center of the
sphere.
AB is a diameter.
CB & AC are radii.
DE & AB are chords.
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
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.
Ex: The circumference of a great
circle of a sphere is 15.5 m. What
is the surface area of the sphere?
C = 2r
15.5 = 2r
15.5 = 2r
7.75 m = r
S = 4r2
S = 4(7.75)2
S = 4(60.0625)
S = 240.25 m2
Or
754.8 m2
Thm 12.12 – Volume of a Sphere
4 3
V  r
3
Ex: Find the volume of a sphere with a
radius of 3 ft.
4
4
3
V   3   27 
3
3
V = 36 ft3 or 113.1 ft3