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12.6

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Sphere – Set of all point in space equidistant from a given point. Center Radius – a segment from the center to a point on the sphere. Chord – A segment whose endpoints are on the sphere. Diameter – A chord that contain the center.

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The surface area S of a sphere is S = 4 πr 2 Where r is the radius

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EXAMPLE 1 Find the surface area of a sphere SOLUTION S = 4πr 2 = 4π(8 2 ) = 256π ≈ 804.25 Formula for surface area of a sphere. Substitute 8 for r. Simplify. Use a calculator. Find the surface area of the sphere. The surface area of the sphere is about 804.25 square inches. ANSWER

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GUIDED PRACTICE for Examples 1 and 2 2. The surface area of a sphere is 30π square meters. Find the radius of the sphere. 2.71 ANSWER

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EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The diameter of the outer ball is 12 feet. Find the surface area of the outer ball. SOLUTION The diameter of the outer sphere is 12 feet, so the radius is = 6 feet. 12 2

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EXAMPLE 3 Use the circumference of a sphere Use the formula for the surface area of a sphere. S = 4πr 2 = 4π(6 2 )= 144π The surface area of the outer ball is 144π, or about 452.39 square feet. ANSWER

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Great Circle – a cross section of the sphere that contain the center Hemisphere – one half of the circle created by the great circle cross section.

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Approximate the volume of the sphere as the sum of n pyramids each with a volume of V = (1/3)Bh.

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EXAMPLE 4 Find the volume of a sphere SOLUTION The soccer ball has a diameter of 9 inches. Find its volume. Formula for volume of a sphere Substitute. V = πr 3 4 3 = π(4.5) 3 4 3 The diameter of the ball is 9 inches, so the radius is = 4.5 inches. 9 2

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EXAMPLE 4 Find the volume of a sphere = 121.5π ≈ 381.70 Simplify. Use a calculator. The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. ANSWER

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EXAMPLE 5 Find the volume of a composite solid SOLUTION = πr 2 h – ( πr 3 ) 1 2 4 3 = π(2) 2 (2) – π(2) 3 2 3 Substitute. Formulas for volume 2 3 = 8π – (8π) Multiply. Find the volume of the composite solid.

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EXAMPLE 5 Find the volume of a composite solid = π – π 24 3 16 3 8 3 = π Rewrite fractions using least common denominator. Simplify. The volume of the solid is π, or about 8.38 cubic inches. 8 3 ANSWER

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842-843 3-9 odd, 13,17,21-27

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10.6 Surface Area & Volume of Spheres

10.6 Surface Area & Volume of Spheres

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