1. How much concrete? We have a blueprint of the proposed dam, how much concrete will it take to build it? http://www.usbr.gov/mp/ccao/docs/auburn_rpt/

2. What is concrete? The word concrete comes from the Latin word "concretus" (meaning compact or condensed), the perfect passive participle of "concrescere", from "con-" (together) and "crescere" (to grow). http://en.wikipedia.org/wiki/Concret e

3. What is concrete? The Roman Colosseum was constructed from concrete and stone in the years 70-80 AD http://en.wikipedia.org/wiki/Colosseu m

4. What is concrete? Concrete is made from a powder called cement, rocks or gravel called aggregate, and water. http://www.ccanz.org.nz/page/Cements.aspx http://en.wikipedia.org/wiki/Construction_aggregate

5. What is concrete? Concrete may also have other additives to make it stronger, harder or cheaper for specific construction purposes: – Sand & various sizes of rocks – Fly Ash (from burning coal) – Epoxy glue type chemicals for curing – Waterproofing chemicals

6. What is cement? “Portland” cement is the most common type, so named for its similarity to limestone quarried from the English Isle of Portland which was used extensively in London's architecture. http://en.wikipedia.org/wiki/Concret e

7. From Google Earth

8. What is cement? Cement consists of a mixture of oxides of calcium, silicon and aluminium. Portland cement is made by heating limestone (a source of calcium) with clay and grinding this product (called clinker) with a source of sulfate (most commonly gypsum). http://en.wikipedia.org/wiki/Concret e

9. What is cement? The important thing to know about cement is that a chemical reaction occurs when water is added to it, this results in heat through a process called curing. Concrete doesn't “dry” like glue, in fact concrete can become hard even when submerged in water! http://en.wikipedia.org/wiki/Concret e Ca 3 SiO 5 + H 2 O → (CaO)·(SiO 2 )·(H 2 O)(gel) + Ca(OH) 2

10. What is concrete? The mixture of concrete should be done by mass (after all we're talking about chemistry here), but for ease of calculation we will use an old rule of thumb for mixing by volume 1 water : 2 cement : 3 gravel http://matse1.matse.illinois.edu/concrete/bm.htm l

11. How much to buy? If we need 6,000 cubic yards of concrete for a project. How much water, cement and aggregate will we need to procure? Remember: 1 water : 2 cement : 3 gravel

12. How much to buy? Write an equation using our extended ratio: 1x + 2x + 3x = 6,000 yds 3 6x = 6,000 x = 1,000 We introduce a variable x that can be thought of as a scale factor for the extended ratio.

13. How much to buy? So we will need to procure: 1x = 1(1000) = 1,000 yds 3 of water 2x = 2(1000) = 2,000 yds 3 of cement 3x = 3(1000) = 3,000 yds 3 of aggregate Note: 1 cubic yard ≈ 202 US gallons

14. What's the volume? http://www.usbr.gov/mp/ccao/docs/auburn_rpt/

15. What's the volume? Here is a cross- section of the proposed dam. Imagine cutting through the dam and looking at the exposed side.

16. What's the volume? Now we need to find the width and height of this triangle using the scale at the top.

17. What's the volume? First, we measure the scale of the drawing. It looks like 2.1 cm equals 100 ft.

18. What's the volume? Next, we measure the height of the triangular cross- section: 14.5 cm

19. What's the volume? Last, we measure the width of the triangular cross- section: 11.2 cm

20. What's the volume? Now calculate the height: And the width:

22. What's the volume? To find the area of a triangle, we multiply the base times the height then divide by two.

23. What's the volume? Now to find the volume of a triangular prism, we multiple the area of the triangular base times the prism's length. So how long is this section of the dam?

24. What's the volume? Section C-C is 980 ft long total.

25. What's the volume?

26. Last, but not least. We wanted the volume of concrete in cubic yards instead of cubic feet. 1 yard = 3 feet 1 square yard = 9 square feet 1 cubic yard = 27 cubic feet

27. What's the volume? The volume of concrete needed to construct sections of the dam labeled C-C is about:

28. What's the volume? Now try to find the volume in the other sections of the dam: A-A, B-B, D-D and E-E. Then add the volumes of all 5 cross sections together for an estimate of the total concrete.