Transcript Cylinders and Cones

Spheres
Definition:
In space, the set of all points that are a given distance
from a given point, called the center.
A sphere is formed by revolving a circle about its diameter.
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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.
Diameter
Tangent
Chord
Radius
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Surface Area & Volume of Sphere
Surface Area (SA) = 4 π r2
Volume (V) =
4 3
r
3
r
Example: Find the surface area and volume of the sphere.
S . A  4  12  576 cm
4
3
3
V   12  2304 cm
3
2
2
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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
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Surface Area & Volume of
Hemisphere
Find the surface area and volume of the following solid
(Hemisphere).
S . A of Sphere  4  102  400
400
2
S . A of Hemisphere 
 200 cm
2
4
V of Sphere   103  1333.3
3
1333.3
V of Hemisphere 
 666.7 cm3
2
10 cm
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