4-7-15 Unit 10 Surface Areas and Volumes 1 Spheres.

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Presentation transcript:

Unit 10 Surface Areas and Volumes 1 Spheres

Spheres 2 A sphere is formed by revolving a circle about its diameter. In space, the set of all points that are a given distance from a given point, called the center. Definition:

Spheres – special segments & lines 3 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. Radius Chord Diameter Tangent

Surface Area & Volume of Sphere 4 Volume (V) = Leave answers in terms of π Surface Area (SA) = 4 π r 2 r Example:Find the surface area and volume of the sphere. 12 cm

Great Circle & Hemisphere 5 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

Surface Area and Volume Hemisphere 6 Surface area of hemisphere = 3 π r 2 Volume of Hemisphere = 2/3 π r 3

Surface Area & Volume of Hemisphere 7 Surface area of hemisphere = 3 π r 2 = 3 π (10) 2 = 300 π cm 2 Volume of Hemisphere = 2/3 π r 3 = 2/3 π (10) 3 = 2000/3 π cm 3 10 cm Find the surface area and volume of the following solid (Hemisphere).