1. SPHERES Surface Area and Volume Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

2. The Geometric Solids

3. SPHERE

4. HEMISPHERE: Half a sphere PLUS the circular base The circle that encloses the base is the GREAT CIRCLE. If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-section? If a plane cuts a sphere along the center, then the plane contains the great circle. Is the equator In a globe a great circle?

5. How do we obtain the Volume of a sphere? https://www.youtube.com/watch?v=h4j8l3p22e8 Video 1

6. How do we obtain the Volume of a sphere? https://www.youtube.com/watch?v=YNutS8eIhEs Video 2

7. Volume of a Sphere Volume of a sphere with radius r

8. Example:

9. How do we obtain the Surface Area of a sphere? https://www.youtube.com/watch?v=cAxHYFRx1Fs Video 3

10. How do we obtain the Surface Area of a sphere? Video 4 https://www.youtube.com/watch?v=xuPl_8o_j7k

11. How do we obtain the Surface Area of a sphere?

12. Surface Area of a Sphere Surface Area of a sphere with radius r How many circle areas cover the sphere?

13. Example:

14. Sphere Surface Area Volume Given a sphere with radius r

15. Solve for the VOLUME and Surface Area:

18. Solve for the unknown and Surface Area:

19. Solve for the unknown: