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Bellwork

Clickers. Bellwork. 8. Find the surface area of the following object

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Bellwork

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  1. Clickers Bellwork 8 Find the surface area of the following object A new stormwater collection culvert is being built near your home. The hole it will be built in is 20’ long by 15’ wide by 10’ deep. The walls of the culvert will be 6 inch thick concrete. How many cubic feet of water can the culvert hold? 3 4

  2. What is the surface area of the object In Use 8 4 3

  3. A new stormwater collection culvert is being built near your home. The hole it will be built in is 20’ long by 15’ wide by 10’ deep. The walls of the culvert will be 6 inch thick concrete. How many cubic feet of water can the culvert hold? Bellwork Solution 14 15 19 20 9.5 10

  4. Volumes of Prisms & Cylinders Section 12.4

  5. The Concept • Up until now we’ve been discussing the concept of Surface Area • Today we’re going to move a step further to discuss the concept of Volumes • We’re going to begin this discussion by examining the volumes of prisms and cylinders

  6. Let’s begin with some postulates that are common sense Postulate 27 Volume of a Cube The volume of a cube is the cube of the length of its side Postulate 28 Volume Congruence Postulate If two polyhedra are congruent, then they have the same volume Postulate 29 Volume Addition Postulate The volume of a solid is the sum of the volumes of all its nonoverlapping parts Postulates

  7. In order to develop a formula that works for all prisms and solids, we look towards the similarities between the formulas for a volume of a prism and that of a cylinder Volume Formula r h h w l

  8. Find the volume of the object below Example 10 8 6

  9. Find the volume of the object below Example

  10. Find the volume of the object below Example

  11. Theorem 12.8 Cavalieri’s Principle If two solids have the same height and the same cross sectional area at every level, then they have the same volume Cavalieri (not Cavalry) What? This principle allows us to solve problems involving oblique objects

  12. Find the volume of the object below Example

  13. What is the volume of the object 5 In Use 10

  14. 5 What is the volume of the object 4 In Use 8

  15. What is the volume of the object In Use

  16. A rain barrel is being used to collect rainwater for watering flowers as part of the Rain Gardens initiative. The barrel is a cylinder with an outside diameter of 24 inches. The width of the barrel’s wall is 1 inch and it’s height is 54 inches. How much water will it hold? In Use

  17. In order to develop a formula that works for all pyramids and cones, we look towards the similarities between the formulas for a volume of a prism and that of a cylinder Volume Formula h

  18. Find the volume of the object below Example

  19. Find the volume of the object below Example 8 6 4

  20. Find the volume of the object below Example 10 h=12 a=6

  21. Find the volume of the object below Example 11

  22. What is the volume of an object that is has a circular base of radius 6”, keeps that cross section for 10” and then comes to a point after 7”? Example

  23. Figure the volume of the interior of this concrete tepee Example 50’ d=20’

  24. Homework 12.4 1-3, 7-14, 16-32 even 12.5 1, 4-36 mult4

  25. Naming scheme applied to solids • Euler’s Theorem • Cross Sections Most Important Points

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