- - AGRICULTURE CORE CURRICULUM - - (CLF2000) Advanced Core Cluster: AGRICULTURAL MECHANICS (CLF2150) Unit Title: MEASUREMENTS ___________________________________________________________________________ (CLF2157) Topic: WEIGHTS & MEASURES Time Year(s) 3 Hours 1 / 2 / 3 / 4 ___________________________________________________________________________ Topic Objectives: Upon completion of this lesson, the students will be able to: Learning Outcome #: (C-3) - Calculate and solve basic measurement problems, including calculation of board feet, cubic measurements, and standard liquid measurements. (C-4) - Differentiate between U.S. Customary and metric measurement units (in linear, area, and volumetric measurements). (C-6) - Calculate and solve basic measurement problems, including weight. Special Material and Equipment: 25' measuring tape, a large graduated cylinder References: Higgs, R., Heidenreich, C., Loberger, R., Cropp, R., & Mitchell, M. (1981). AGRICULTURAL MATHEMATICS: PROBLEMS IN PRODUCTION, MANAGEMENT, MARKETING, MECHANIZATION, ENVIRONMENTAL QUALITY (2nd ed.). Danville, IL: Interstate Printers & Publishers. Hokanson, C. M. (1984). APPLIED PROBLEMS IN MATHEMATICS FOR AGRICULTURE. Danville, IL: Interstate Printers & Publishers. Evaluation: Quiz by instructor. TOPIC PRESENTATION: WEIGHTS AND MEASURES A. Liquid and Dry Measures of Capacity and Weight Units 1. Their Use in the Agriculture Industry a. Different units of weight and measure are utilized by various trades, occupations, and professions. b. Standards of liquid measure use units both similar to and different from dry measures (see lesson 2151). 1) The standard dry units, pints and quarts, are also used in liquid measure. 2) The most common unit of liquid measure in agricultural marketing is the gallon. a) Water, oil, farm chemicals, and many other products are marketed in gallons. b) Because larger containers reduce packaging and marketing costs, milk--once sold primarily in quarts--is now sold mostly in half gallons and gallons. c. Standard dry measures such as pints, quarts, and pecks are common in agriculture. d. Most of the common dry agricultural products have standard weights for a known volume such as cubic feet, board feet, bushels, and barrels. e. The pound is the basis for most marketing in U.S. agriculture. 2. Standard Measures of Capacity a. Liquid Measure 1) English Liquid Measure a) 1 ounce (oz) = .25 gill b) 4 gills (gi) = 1 pint c) 1 pint (pt) = 16 fluid ounces (fl oz) d) 1 quart (qt) = 2 pints e) 1 gallon (gal) = 4 quarts f) 1 barrel (bbl) = 31.5 gallons g) 1 hogshead (hhd) = 2 barrels 2) Metric Liquid Volume a) 1 kiloliter (kl) = 1,000 liters (L) b) 1 hectoliter (hl) = 100 liters c) 1 decaliter (dkl) = 10 liters d) 1 liter (l) = 1 liter e) 1 deciliter (dl) = 0.1 liter f) 1 centiliter (cl) = 0.01 liter g) 1 milliliter (ml) = 0.001 liter b. English Dry Measure 1) 1 quart (qt) = 2 pints (pt) 2) 1 small measure = 2 quarts 3) 1 peck (pk) = 8 quarts 4) 1 bushel = 4 pecks 3. English (Avoirdupois) and Metric Weights a. English Weights 1) 7000 grains (gr) = 1 pound 2) 1 ounce (oz) = 437.5 gr 3) 1 pound (lb) = 16 oz 4) 1 hundredweight (cwt) = 100 lb 5) 1 short ton (T) = 2000 lb 6) 1 long ton = 2240 lb b. Metric Weights 1) 1 microgram (mcg) = 0.000001 gram 2) 1 milligram (mg) = 0.001 gram 3) 1 centigram (cg) = 0.01 gram 4) 1 decigram (dg) = 0.1 gram 5) 1 gram (g or gm) = 1 gram 6) 1 decagram (dkg) = 10 grams 7) 1 hectogram (hg) = 100 grams 8) 1 kilogram (kg) = 1000 grams 9) 1 metric ton (t.) = 1000 kilograms B. Dry and Liquid Measure of Capacity and Weight Conversions 1. Conversion Procedures a. The solution to many practical problems in agricultural mechanics requires the conversion of cubic measures of volume to dry or liquid measures of capacity; dry and liquid measures to weights; and the reverse: weight to capacity to volume. b. Once the volume of a particular container or structure is determined, the volume can be changed to a measurement unit or weight of a particular dry or liquid commodity in question. 2) To change a larger unit of dry or liquid measure or weight to a smaller unit, one multiplies. 3) To change a smaller unit of dry or liquid measure or weight to a larger number, one divides. c. To convert cubic volumes to measures of capacity and weight, refer to measurement conversion tables. 1) Cubic Measures of Volume and Liquid Measures of Capacity a) English System - 1 cubic foot = 7.5 gallon - 1 gallon = 231 cubic inches b) Metric System - l liter = 1.0567 quarts - 1 gallon = 3.7853 liters 2) Cubic Measures of Volume and Dry Measures of Capacity a) English System - 1 cubic foot = .8 bushels - 1 bushel = 1.25 cubic feet b) Metric System - 1 liter = 0.908 dry quart - 1 bushel = 35.2383 liters 3) Liquid and Dry Measures of Capacity and Weight a) Liquids - 1 gal water = 8.339 lbs - 1 cu ft water = 62.5 lbs - 1 gal skim milk = 8.65 lbs - 1 gal average milk = 8.6 lbs - 1 cu ft concrete = 100 lbs - 1 gal gasoline = 6 lbs b) Dry Commodities and Materials - 1 bu apples = 60 lbs - 1 bu barley = 49 lbs - 1 bu coal = 80 lbs - 1 bu shelled corn = 56 lbs - 1 bu millet = 50 lbs - 1 bu peaches = 48 lbs - 1 bu soybeans = 60 lbs - 1 bu walnuts = 50 lbs - 1 bu wheat = 60 lbs B. Determining Capacities 1. Finding the Dry Capacity of a Bin a. Many agricultural commodities are stored in bins, grain being the most common. b. Each grain variety has an approximate weight per bushel. c. Once the volume of a particular container is determined, dry measure and weight conversion tables can be used to change the volume to the weight or number of bushels of the commodity. Example: A grain bin is 10' long, 10' wide, and 12' high. How many tons of wheat are in the bin? Step 1 - Find the volume of the bin. V = lwh V = 10 X 10 X 12 V = 1200 cu ft Step 2 - Convert cu ft to bushels (refer to conversion table). no. of bu = cu ft X .8 no. of bu = 1200 X .8 no. of bu = 960 Step 3 - Convert bu of wheat to pounds (refer to conversion table). no. of lb = bu X 60 no. of lb = 960 X 60 no. of lb = 57,600 Step 4 - Convert lb to tons (refer to conversion table). no. of T = no. of lb/2000 no. of T = 57,600/2000 no. of T = 28.8 2. Finding the Dry Capacity of a Cylinder a. Many dry, agricultural commodities are stored in barrels, cylindrical bins, and silos. b. To find the capacity of one of these cylinders, first determine the volume in cubic measure, then convert it to bushels or to the weight of the commodity filling the space. Example: There is 10 ft of shelled corn remaining in a silo that has a radius of 8 ft. Determine how many tons of silage are left. Step 1 - Find the volume of the remaining shelled corn. 2 V = pi r h 2 V = 3.14 X 8 X 10 V = 3.14 X 64 X 10 V = 3.14 X 640 V = 2009.6 cu ft Step 2 - Convert cu ft to bushels. no. of bushels = cu ft X .8 no. of bushels = 2009.6 X .8 no. of bushels = 1607.68 Step 3 - Convert bu to pounds. no. of lb = bu X 56 no. of lb = 1607.68 X 56 no. of lb = 90,030 Step 4 - convert lb to tons. no. of T = no. of lb/2000 no. of T = 90,030/2000 no. of T = 45.02 3. Finding the Liquid Capacity of a Cylinder a. Cylinders are also used to store and transport liquids in the agricultural industry. b. Milk is transported to processing plants in cylindrical tank trucks. c. Regardless of the liquid involved, one must first find the volume before determining the liquid measure or the weight. Example: A milk truck has a cylindrical tank 5 ft in diameter and 12 ft long. Determine how many gallons of milk it holds and how much that milk weighs. Step 1 - Find the volume of the cylindrical tank. 2 V = pi X r X h 2 V = 3.14 X 2.5 X 12 V = 3.14 X 6.25 X 10 V = 3.14 X 75 V = 235.5 cu ft Step 2 - Convert cu ft to gallons. no. of gal = cu ft X 7.5 no. of gal = 235.5 X 7.5 no. of gal = 1766.25 Step 3 - Convert gal to pounds. no. of lb = gal X 8.6 no. of lb = 1766.25 X 8.6 no. of lb = 15,189.75 Step 4 - convert lb to tons. no. of T = no. of lbs/2000 no. of T = 15,189.75/2000 no. of T = 7.59 4. Finding Board Feet a. The board foot (bd ft) is the unit of measure for lumber. b. A board foot is a board 1 inch thick, 12 inches wide, and 12 inches long. c. The cubic measure equivalent of a board foot is 144 cu in. d. Standard size pieces of lumber can be easily calculated by visualizing the board feet included. 1) A board 1" by 12" and 6' long will contain 6 bd ft. 2) A board 1" by 6" and 6' long will contain 3 bd ft. 3) A board 2' by 12" and 6' long will contain 12 bd ft. e. The following formula can be applied to any size lumber as long as its total length is given in feet. Bd ft = No. pcs. X thickness X width X length divided by 12 f. The board foot formula reads, "Board feet are equal to the number of pieces of lumber times the thickness of each piece in inches; times the width of each piece in inches; times the length of each piece in feet; divided by 12." 1) Lumber less than 1 inch thick is calculated as 1 inch. 2) Lumber 1 inch or thicker is calculated according to its actual size. 3) When the lumber size contains fractions, change measurement to an improper fraction and proceed according to the formula. Example: Find the bd ft in 8 pieces of lumber that measure 2" X 8" X 10.' Bd ft = No. pcs. X t X w X l divided by 12 Bd ft = 8 X 2 X 8 X 10 divided by 12 Bd ft = 106.67 bd ft _________________________________________________________ ACTIVITY: 1. Determine the cubic volume of a soda can; convert the cubic measure of volume to a liquid measure of capacity; convert the liquid measure to its equivalent weight in water; weigh the can filled with water; and compare the calculated weight with its actual weight. 2. Weigh a bag of grain and determine how many bushels and cubic feet it would fill. Convert the results to metric volume and test the calculations in a graduated cylinder. NOTE: The amount of grain used does not have to be large. _________________________________________________________ 6/27/91 OLR/tf #%&C