1. 3-D Solids and formulas Unit 7-5

2. 3-D solid figures Cylinder Triangular prism Rectangular prism Cone Pyramid Sphere Fill in 3-D chart

3. Vocabulary Polyhedron Formed by 4 or more polygons that intersect only at their edges. Is this a polyhedron?

4. Euler’s Formula For any polyhedron with V(ertices), E(dges), and F(aces) V – E + F = 2 10-15+ 7 = 2 2

5. Euler’s Formula For any polyhedron with V(ertices), E(dges), and F(aces) V – E + F = 2 0 - 2 + 3 = 2 1 NOT a Polyhedron

6. Diagonals inside prisms

7. Diagonal of a right rectangular prism The length of a diagonal (d) of a right rectangular prism with length (l) and width (w), and height (h) Find the length of the diagonal of a 3 in. by 4 in. by 5 in rectangular prism.

8. Graphing in 3-D There are 3 axis when graphing in 3-D X-axis (horizontal), Y-axis(vertical), Z-axis (3-D) Points are (x, y, z) X axis Y axis Z axis

9. Graphing in 3-D More traditional 3-D graphing Points are (x, y, z) Y axis Z axis X axis Solid lines are positive and broken lines are negative

10. Graphing in 3-D

11. Video on Graphing 3-D https://search.yahoo.com/search;_ylt=AwrBT7XW7ThVfhAA4nVXNyo A;_ylc=X1MDMjc2NjY3OQRfcgMyBGZyA3lmcC10LTI1MARncHJpZ AN0MmdZWkxIWlQ4eU5adEl2NVJ4M3hBBG5fcnNsdAMwBG5fc3V nZwMzBG9yaWdpbgNzZWFyY2gueWFob28uY29tBHBvcwMwBHBxc 3RyAwRwcXN0cmwDBHFzdHJsAzE5BHF1ZXJ5A2hvdyB0byBncmFw aCBpbiAzLUQEdF9zdG1wAzE0Mjk3OTQzNTQ- ?p=how+to+graph+in+3-D&fr2=sb-top-search&fr=yfp-t-250&fp=1

12. Distance and Midpoint in 3-D d = midpt =

13. Example # 1 Find the distance and midpoint (in 3-D) given points: A (9, 0, 5) and B ( 6, 0, 12) Example # 2 Find the height of a rectangular prism with an 8 ft by 12 ft base and an 18 ft diagonal.