Agriculture Mechanics A3-5 Planning and Placing Concrete - Illinois ...

Agriculture Concepts:Volumes are used frequently in agricultural construction and production, especially whendetermining the amount of concrete needed for a particular job. Ordering too muchconcrete costs extra money, and the excess concrete cannot be taken back to the plant.Ordering too little can cause delays in construction and require starting the job over.Concrete is usually bought and sold in units of cubic yards.1 cubic yard = 27 cubic feetConcrete pads are used in grain storage systems to create strong bases for metal grainbins. Grain is typically measured in bushels, with 1 bushel of dry corn weighing 56 poundsand taking up 1.24 cubic feet of space. Grain storage is a crucial part of marketingbecause it allows a farmer to store and sell grain at better prices.Guided Practice Exercises:ANSWER KEY19 ft1. r=(36÷2)+12 ftr=192. V c = ×r 2 ×hV c = ×19 2 ×2V c = 2,267.08 ft 32,267.08 ÷ 27 = 83.97 yd 33. V cyl = ×18 2 ×44V cyl = 44,786.54 ft 3 ÷ 1.24 ft 3 /buV cyl = 36,118.18 buV cone = 1 / 3 ×18 2 ×8V cone = 2,714.34 ft 3 ÷ 1.24 ft 3 /buV cone = 2,188.98 buV bin =V cyl +V coneV bin = 36,118.18 + 2,714.34V bin = 38,832.52 bu4. No, the extra corn will not fit. There will be almost 6,000 bushels that will not fit.120,000 – 38,000 = 82,000 buV cone = 1 / 3 × ×(120÷2) 2 ×25V cone = 94,247.78 ft 3 ÷ 1.24 ft 3 /buV cone = 76,006.27 buCOMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 2Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

1.Independent Practice Exercises:ANSWER KEYr = 27 ft, h = 2 ftr = 16 ft, h = 2 ftr = 13 ft, h = 2 ft2. V c = ×r 2 ×hV c = ×27 2 ×2V c = 4,580.44 ft 34,580.44 ÷ 27 = 169.64 yd 3V c = ×r 2 ×hV c = ×16 2 ×2V c = 1,608.50 ft 31,608.50 ÷ 27 = 59.57 yd 3V c = ×r 2 ×hV c = ×13 2 ×2V c = 1,061.86 ft 31,061.86 ÷ 27 = 39.33 yd 33. a. 52-foot diameterV cyl = ×26 2 ×24V cyl = 50,969.20 ft 3 ÷ 1.24 ft 3 /buV cyl = 41,104.19 buV cone = 1 / 3 ×26 2 ×6V cone = 4,247.43 ft 3 ÷ 1.24 ft 3 /buV cone = 3,425.35 buV bin =V cyl +V coneV bin = 41,104.19 + 3,425.35V bin = 44,529.54 bub. 30-foot diameterV cyl = ×15 2 ×24V cyl = 16,964.60 ft 3 ÷ 1.24 ft 3 /buV cyl = 13,681.13 buV cone = 1 / 3 ×15 2 ×6V cone = 1,413.72 ft 3 ÷ 1.24 ft 3 /buV cone = 1,140.09 buCOMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 3Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

V bin =V cyl +V coneV bin = 13,681.13 + 1,140.09V bin = 14,821.22 buc. 24-foot diameterV cyl = ×12 2 ×24V cyl = 10,857.34 ft 3 ÷ 1.24 ft 3 /buV cyl = 8,755.92 buV cone = 1 / 3 ×12 2 ×6V cone = 904.78 ft 3 ÷ 1.24 ft 3 /buV cone = 729.66 buV bin =V cyl +V coneV bin = 8,755.92 + 729.66V bin = 9,485.58 bu4. V cyl = ×r 2 ×hV cyl = ×27 2 ×2V cyl = 4,580.44 ft 3V cone = 1 / 3 ×27 2 × 1.5V cone = 1,145.11 ft 3V pad =V cyl –V coneV pad = 4,580.44 – 1,145.11V pad = 3,435.33 ft 3 ÷27ft 3V pad = 127.23 yd 3a. Putting in a conical depression would be more economical (cheaper) because itwould save 42 cubic yards of concrete.b. The shape would allow grain to flow more easily during removal.COMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 4Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

Guided Practice Exercises:Name: _______________________________________________Alex is planning to build a new circular grain bin.The grain bin will be 36 feet in diameter and 44feet high, with a top cone 8 feet high. Theconcrete pad should be 1 foot larger than thestructure and 24 inches thick. How much concretedoes Alex need to order?Shape Volume FormulaCylinder ×r 2 ×hCone 1/ 3 ×r 2 ×h1. Draw a diagram of the pad for the grain bin, showing the radius and the height.2. What is the volume of concrete, in cubic yards, needed to pour the pad?COMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 5Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

3. How much corn, in bushels, can the bin hold if it is filled to capacity, including themounding at the top? (Corn weighs 56 lb/bu, and 1 bu takes up 1.24 ft 3 of space.)4. After building the grain bin, Alex harvested a total of 120,000 bushels of corn. Hedecided to pile the extra corn on a circular concrete pad he already had and cover itwith a tarp. Assuming he stored 38,000 bushels in his bin, will the rest of the cornfit on his 120-foot-diameter pad if it can safely be piled 25 feet high?COMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 6Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

Name: _______________________________________________Independent Practice Exercises:Alex is expanding his grain-handling facility. He isplanning to build three more bins to hold hisgrain—one large bin 52 feet in diameter and twosmaller ones 30 feet and 24 feet in diameter.Each bin will be 24 feet tall with a 6-foot cone atthe top. The pad for each bin should be 24 inchesthick and 1 foot larger around than the bin.Shape Volume FormulaCylinder ×r 2 ×hCone 1/ 3 ×r 2 ×h1. Draw a diagram of the pad for each grain bin, showing the radius and the height.2. What is the volume of concrete, in cubic yards, needed to pour the three differentpads?COMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 7Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018

3. How much corn, in bushels, can each bin hold if it is filled to capacity, including themounding at the top? (Corn weighs 56 lb/bu, and 1 bu takes up 1.24 ft 3 of space.)4. How much concrete will be needed for the largest bin if a conical depression is putin the pad so that the center of the pad will be only 6 inches thick but the walls willremain 24 inches thick? Think of two reasons why this would be a better designthan a flat, circular pad.COMMON CORE MATH INTEGRATION ACTIVITY: AMT A3–5: Planning and Placing Concrete Page 8Copyright © by CAERT, Inc. | Reproduction by subscription only. | www.MyCAERT.com | A090018