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Chapter 12 12.6

Chapter 12 12.6. Surface Area and Volume of Spheres. Definition of a Sphere. The locus of all points in space that are a given distance from a point That point is called the center of the sphere The Radius of the sphere is a segment from the center to a point on the sphere.

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Chapter 12 12.6

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  1. Chapter 1212.6 Surface Area and Volume of Spheres

  2. Definition of a Sphere • The locus of all points in space that are a given distance from a point • That point is called the center of the sphere • The Radius of the sphere is a segment from the center to a point on the sphere. • A Chord of the sphere is a segment with endpoints on the sphere • The Diameter of a sphere is a chord that contains the center of the sphere

  3. Examples Radius Diameter Center Chord

  4. Sphere Has a center Has a diameter Has chords Contained in space Circle Has a center Has a diameter Has chords Lies in a plane Spheres VS Circles

  5. More about circles • When a plane intersects a sphere the intersection is a • Circle or a Point • Great Circle • A circle that cuts the sphere into two congruent halves called hemispheres and contains the center of the sphere

  6. Theorem 12.11: Surface Area of a Sphere S = 4r2 • S is the surface area • r is the radius of the sphere

  7. Theorem 12.12: Volume of a Sphere • V is the volume of the sphere • r is the radius of the sphere

  8. Find the Surface area and volume of the sphere • Volume • Surface Area • S = 4r2 • Find r: • Find r: • Fill in formula • Fill in formula

  9. Find the Surface area and volume of the sphere • Volume • Surface Area • S = 4r2 • Find r: • Find r: • Fill in formula • Fill in formula

  10. Find the Surface area and volume of the sphere • Volume • Surface Area • S = 4r2 • Find r: • Find r: • Fill in formula • Fill in formula

  11. Fill in the chart 20 400 18 1296  7776  24 48  18432  5 10  100 

  12. Find the surface area of the following figure • Area of the cylinder less the top base plus the area of the hemisphere Area of Cylinder less the top base Half the area of the sphere

  13. Find the volume of the following figure • Volume of the cylinder less the volume of the hemisphere Half the volume of the sphere Volume of Cylinder

  14. Homework #74Pg 762-764 10-17, 20-29, 35-40

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