1. Volume & Surface Area State Standard: 9-12.G.GMD.1. -- Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

2. What Will We Cover Today?  Review Previous Vocabulary  New Useful Equations For Volume and Surface Area  Discover What Cavalieri’s Principle and How to Use it. What Will We Be Able To Do After Today’s Lesson?  Find the Surface Area and Volume of Cylinders, Cones, and Spheres.  Use Cavalieri’s Principle #mathclass#mathclass

3. Who can tell me what these terms mean? VolumeArea Surface Area RadiusPerimeter#mathclass#mathclass

4. The Circle Circumference of a Circle: C = 2*πr Area of a Circle: A = π*r^2 Ex: Gigantic Googly Eyes #mathclass#mathclass

5. The Cylinder Two circles who’s planes are parallel and are separated by some distance ‘h.’ To find area of a cylinder simply find the area of one of its ends and multiply it by the height, ‘h.’ Volume of a Cylinder: V = h * π * r^2 Ex: Can of Baked Beans #mathclass#mathclass

6. The Cone To find the volume of a cone, use the same formula as a cylinder, but multiply by 1/3. Volume of a Cone: V = (1/3) * h * π * r^2 Ex: Traffic Cone #mathclass#mathclass

7. The Sphere To find the volume and surface area of a sphere, all we need is its radius. Volume of a Sphere: V = (4/3) * π * r^3 Surface Area of a Sphere: SA = 4 * π * r^2 Ex: Orange and Tennis Ball #mathclass#mathclass

8. Introduction to Cavalieri’s Principle Bonaventura Cavalieri observed that figures (solids) of equal height and in which all corresponding cross sections match in length (area) are of equal area (volume). For example, take a regular polygon equal in area to an equilateral triangle; erect a pyramid on the triangle and a cone-like figure of the same height on the polygon; cross sections of both figures taken at the same height above the bases are equal; therefore, by Cavalieri's theorem, so are the volumes of the solids. #mathclass#mathclass

9. Video On Cavalieri’s Principle Cavalieri's Principle - (Video would not embed into PowerPoint)Cavalieri's Principle #mathclass#mathclass

10. Review Video Volume and Surface Area of a Sphere - (Video would not embed into PowerPoint)Volume and Surface Area of a Sphere #mathclass#mathclass