12 6 surface area and volume of spheres l.
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12.6 Surface area and Volume of Spheres

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12.6 Surface area and Volume of Spheres - PowerPoint PPT Presentation


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12.6 Surface area and Volume of Spheres. Definitions . Sphere: is the locus pf points in space that are a given distance from a point. The center of the sphere is that point. Radius of a sphere: is a segment from the center to a point on the sphere.

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definitions
Definitions
  • Sphere: is the locus pf points in space that are a given distance from a point. The center of the sphere is that point.
  • Radius of a sphere: is a segment from the center to a point on the sphere.
  • Chord of a sphere: is a segment whose endpoints are on the sphere.
  • Diameter: is a chord that contains the center.
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Cont.
  • If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a Great Circle.
  • Hemisphere: two congruent halves of a sphere.
theorems
Theorems
  • 12.11: The Surface area S of a sphere with radius r is S=4πr²
  • 12.12: The volume V of a sphere with the radius r is V=4/3πr³
examples
Examples

Find the Surface Area

S=4πr²

S= 4(3.14)(22²)

S=4(1519.76)

S=6079.04inches

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Find Volume of Sphere

V=4/3πr³

V=4/3(3.14)(22³)

V=4/3(33434.72)

V=44579.626