12.6 SA & Vol of Spheres

12.6 SA & Vol of Spheres - 12.6 Surface Area&...

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Unformatted text preview: 12.6 Surface Area & Volume of Spheres of p. 759 Definitions Definitions • Sphere – the locus of points in space that space are a given distance from a given point. (looks like a ball) (looks • Center of a Sphere – the given point in the middle. middle. • Radius of a Sphere – segment from the center to a point on the sphere. center • Chord of a Sphere – a segment whose endpoints are on the sphere. endpoints • Diameter of a Sphere – a chord that goes through the center. through Parts of a Sphere Parts C is the center of the is sphere. sphere. AB is a diameter. CB & AC are radii. DE & AB are chords. A C B E D Thm 12.11 – Surface Area of a Sphere Thm S = 4π 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 Find with a diameter of 8 cm. with S = 4π (4)2 S = 4π (16) S = 64π cm2 More Definitions More • Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center. center. • Hemisphere – ½ of a sphere. ** Every great circle splits a sphere into 2 ** hemispheres. hemispheres. Ex: The circumference of a great Ex The circle of a sphere is 15.5π m. What circle is the surface area of the sphere? is C = 2π r 15.5π = 2π r 15.5 = 2r 7.75 m = r S = 4π r2 S = 4π (7.75)2 S = 4π (60.0625) S = 240.25π m2 Or 754.8 m2 Thm 12.12 – Volume of a Sphere Thm 43 V = πr 3 Ex: Find the volume of a sphere with a Find radius of 3 ft. radius 4 4 3 V = π ( 3) = π ( 27 ) 3 3 V = 36π ft3 or 113.1 ft3 Assignment Assignment ...
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This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

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