1. SPHERES Surface Area and Volume
Geometry
Regular Program SY
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 a plane cuts a sphere along the center, then the plane contains the great circle.
If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-section?
Is the equator In a globe a great circle?

5. Volume of a sphere with radius r

6. Example:

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

8. Example:

9. Given a sphere with radius r
Volume
Surface Area

10. Solve for the VOLUME and Surface Area:

11. Solve for the VOLUME and Surface Area:

12. Solve for the VOLUME and Surface Area:

13. Solve for the unknown and Surface Area:

14. Solve for the unknown:

15. Solve for the unknown:

16. Solve for the unknown: