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Warm - up

Warm - up. 1. 2. Surface Area and Volume of Spheres. Section 6.9. Standards. MM2G4. Students will find and compare the measures of spheres. a. Use and apply surface area and volume of a sphere.

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Warm - up

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  1. Warm - up 1. 2.

  2. Surface Area and Volume of Spheres Section 6.9

  3. Standards • MM2G4. Students will find and compare the measures of spheres. • a. Use and apply surface area and volume of a sphere. • b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

  4. Unit: What measurements can I make on curved shapes? • Lesson: • What if the surface is curved?

  5. radius center Vocabulary • Sphere – the locus of points in space that are a given distance from a point. The point is called the center of the sphere. • Radius of a sphere – a segment from the center to a point on the sphere.

  6. chord diameter Vocabulary • Chord of a sphere – a segment whose endpoints are on the sphere. • Diameter of a sphere – a chord that contains the center.

  7. Theorem: Surface Area of a Sphere • The surface area S of a sphere with radius r is S = 4πr2

  8. Vocabulary • Great Circle – The intersection of a sphere and a plane that contains the center of the sphere. • Hemisphere – half of a sphere, formed when a great circle separates a sphere into two congruent halves.

  9. S = 4πr2 S = 4π(122) S = 576πcm2 S = 4πr2 S = 4π(42) S = 64πcm2 The surface area does not triple!

  10. C = 2πr 15.5π = 2πr r = 7.75 S = 4πr2 S = 4π(7.752) S = 240.25πm2 S ≈ 754.77 m2

  11. S = 4πr2 S = 4π(52) S = 100πin2 S ≈ 314.16 in2

  12. Theorem: Volume of a Sphere • The volume V of a sphere with radius r is

  13. Example 4 • Find the volume of a sphere with a radius of 3 feet. Leave answer in terms of π. V = 36πft3

  14. Ticket Out the Door • If a sphere has a radius of 3, what is it’s surface area and volume? • If we double the radius to 6, what is the new surface area and volume? • Explain the numerical relationship between: • The two surface areas. • The two volumes.

  15. Classwork • Page 239-240 • 2 – 30 Even Homework • Pages 239 - 240 • 1 – 30 Odd

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