2 DefinitionsSphere – 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.
3 C is the center of the sphere. Parts of a SphereC is the center of the sphere.AB is a diameter.CB & AC are radii.DE & AB are chords.CABED
4 Thm 12.11 – Surface Area of a Sphere S = 4r2(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)2S = 4(16)S = 64 cm2
5 More DefinitionsGreat 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.
6 Ex: The circumference of a great circle of a sphere is 16 m Ex: The circumference of a great circle of a sphere is 16 m. What is the surface area of the sphere?S = 4r2S = 4(8)2S = 4(64)S = 256 m2C = 2r16 = 2r16 = 2r8 m = r
7 Ex: Find the volume of a sphere with a radius of 3 ft. Thm – Volume of a SphereEx: Find the volume of a sphere with a radius of 3 ft.V = 36 ft3