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12.6 Surface Area & Volume of Spheres

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Definitions Sphere – the locus of points in space that are a given distance from a given point. (looks like a ball)Sphere – 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.Center of a Sphere – the given point in the middle. Radius of a Sphere – segment from the center to a point on the sphere.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.Chord of a Sphere – a segment whose endpoints are on the sphere. Diameter of a Sphere – a chord that goes through the center.Diameter of a Sphere – a chord that goes through the center.

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Parts of a Sphere C is the center of the sphere. AB is a diameter. CB & AC are radii. DE & AB are chords. C A B D E

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Thm – Surface Area of a Sphere S = 4 r 2 (it takes 4 circles to cover a sphere) Why isnt 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) 2 S = 4 (16) S = 64 cm 2

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More Definitions Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center.Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center. Hemisphere – ½ of a sphere.Hemisphere – ½ of a sphere. ** Every great circle splits a sphere into 2 hemispheres.

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Ex: The circumference of a great circle of a sphere is 16 m. What is the surface area of the sphere? C = 2 r 16 = 2 r 8 m = r S = 4 r 2 S = 4 (8) 2 S = 4 (64) S = 256 m 2

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Thm – Volume of a Sphere Ex: Find the volume of a sphere with a radius of 3 ft. V = 36 ft 3

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