1. Geometric Measurements Christine Knobbe base circumference length height

2. Shapes vs. Figures What are the basic geometric shapes? ◦ Square ◦ Triangle ◦ Circle What are the basic geometric figures? ◦ Cube ◦ Prism ◦ Pyramid ◦ Cone ◦ Sphere ◦ Cylinder

3. Types of measurement What types of terms are associated with geometric measurements? ◦ Area ◦ Perimeter ◦ Circumference ◦ Volume ◦ Surface Area Do you remember the formulas? ◦ Discuss with a partner Why are these separated?

4. Formulas Area ◦ A = L*W, A =  r 2 Perimeter ◦ P = 2L + 2W Circumference ◦ C = 2  r Volume ◦ V=bh, where b is the area of the base Surface Area ◦ S = sum of area of all sides These vary depending on what shape the base is.

5. Formula Exceptions The volume of a couple of geometric figures is tricky! Which are they? ◦ Pyramids and Cones Why do you think so? ◦ They come to a point instead of staying the same shape the entire length like a prism ◦ V = 1/3 bh

6. Practice Problems Get into small groups (3-4) Find the following for each figure: ◦ Surface Area ◦ Volume 7 cm 2 in 5 in 24 m 100 m

7. Practice Solutions Only one dimension is given ◦ So it must be a cube Surface area ◦ S = sum of area of all sides ◦ S = 7 2 + 7 2 + 7 2 + 7 2 + 7 2 + 7 2 ◦ S = 6 * 7 2 = 294 cm 2 Volume ◦ V = bh = L*W*h ◦ V = 7 * 7 * 7 = 343 cm 3 7 cm Volunteers?

8. Practice Solutions 24 m 100 m Volunteers? Surface area ◦ S = sum of area of all sides ◦ S = 2 circles + middle ◦ S = 2 (  r 2 ) + L*h ◦ S = 2 (  (12) 2 ) + 2  (12)*100 ◦ S = 8444.6 m 2 Volume ◦ V = bh =  r 2 *h ◦ V =  (12) 2 * 100 = 45238.9 m 3

9. Practice Solutions 2 in 5 in Volunteers? Volume ◦ V = 1/3 bh = 1/3  r 2 * h ◦ V = 1/3  2 2 * 5 = 20.9 in 3 Surface area ◦ S = sum of area of all sides ◦ S = circle + top ◦ S =  r 2 + oops! ◦ S =  r 2 +  rs ◦ S =  2 2 +  2*  29 ◦ S = 23.3 in 2 S =  r 2 +  rs r h s How do we find s? s 2 = r 2 + h 2 s 2 = 2 2 + 5 2 = 29 s =  29

10. Practical Applications How would you be able to use this in real life? ◦ Discuss in a small group (3-4) Home Improvement ◦ Figuring out the square footage to know how many materials to get (flooring, paint, etc.) Short cuts ◦ Did you know that the shortest flying distance from Florida to the Philippine Islands is a path across Alaska? Object shaping ◦ Ex: cutting wood to get the desired shapes when building furniture Pool shark ◦ Have you ever noticed the angles, measures, and physics involved in the game of pool?

11. Career options Computer graphics Virtual reality Biochemical modeling Facial recognition Engineering ◦ Civil ◦ Mechanical ◦ Computer Cartography ◦ geo sciences ◦ construction Astronomy Contracting Architecture

12. Architect If you could build a colony on the moon, what would you do and why? What figures and shapes would you use?