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1 RULES RELATIVE TO THE CIRCLE TO FIND DIAMETER TO FIND CIRCUMFERENCE TO FIND RADIUS TO FIND SIDE OF AN INSCRIBED SQUARE TO FIND SIDE OF AN EQUAL SQUARE Multiply circumference by Or divide circumference by Multiply diameter by Or divide diameter by Multiply circumference by Or divide circumference by Multiply diameter by Or multiply circumference by Or divide circumference by Multiply diameter by Or divide diameter by.284. Or multiply circumference by Or divide circumference by SQUARE A side multiplied by.442 equals diameter of its circumscribing circle. A side multiplied by equals circumference of its circumscribing circle. A side multiplied by.28 equals diameter of an equal circle. Square inches multiplied by.273 equals circle inches of an equal circle. TO FIND THE AREA OF A CIRCLE TO FIND THE SURFACE OF A SPHERE OR GLOBE Multiply circumference by /4 of the diameter. Or multiply the square of diameter by Or multiply the square of circumference by Or multiply the square of /2 diameter by Multiply the diameter by the circumference. Or multiply the square of diameter by Or multiply four times the square of radius by To find cubic inches in a globe multiply cube of diameter by Any circle whose diameter is double that of another contains four times the area of the other. MATERIALS REQUIRED FOR 00 SQUARE FEET OF SURFACE FOR VARYING THICKNESS OF CONCRETE OR MORTAR C. Cement in sacks. F.A. Fine Aggregate (Sand) in Cu. Ft. C.A. Coarse Aggregate (Pebbles or Broken Stone) in Cu. Ft.

2 UNITS OF VOLUME AND WEIGHT TROY WEIGHT 24 grains = pennyweights 20 pennyweights = ounce 2 ounces = pound (used for weighing gold, silver and jewels) APOTHECARIES WEIGHT 20 grains = scruple 3 scruples = dram 8 drams = ounce 2 ounces = pound AVOIRDUPOIS WEIGHT 27-/3 grains = dram 6 drams = ounce 6 ounces = pound 25 pounds = quarter 4 quarters = hundredweight 2,000 pounds = short ton 2,240 pounds = long ton DRY MEASURE 2 pints = quart 8 quarts = peck 4 pecks = bushel 36 bushels = chaldron LIQUID MEASURE 4 gills = pint 2 pints = quart 4 quarts = gallon 3-/2 gallons = barrel 2 barrels = hogshead TIME MEASURE 60 seconds = minute 60 minutes = hour 28, 29, 30 or 3 days = month 30 days = month (when computing interest) 365 days = year 24 hours = day 7 days = week CIRCULAR MEASURE 60 seconds = minute 60 minutes = degree 4 quadrants = 2 signs 360 degrees = circle 30 degrees = sign 90 degrees = quadrant LONG MEASURE 2 inches = foot 3 feet = yard 5-/2 yards = rod 40 rods = furlong 8 furlongs = statute mile 3 miles = league CLOTH MEASURE 2-/4 inches = nail 4 nails = quarter 4 quarters = yard MARINER S MEASURE 6 feet = fathom 20 fathoms = cable length 7-/2 cable lengths = mile 5,280 feet = statute mile 6,085 feet = nautical mile MISCELLANEOUS 3 inches = palm 4 inches = hand 6 inches = span 8 inches = cubit 2.8 inches = Biblical cubit 2-/2 feet = military step SQUARE MEASURE 44 sq. inches = sq. foot 9 sq. feet = sq. yard 30-/4 sq. yards = sq. rod 40 sq. rods = rood 4 roods = acre 640 acres = sq. mile SURVEYOR S MEASURE 7.92 inches = link 0 sq. chains, or 60 sq. rods = acre 640 acres = sq. mile 36 sq. miles (6 miles sq.) = township 25 links = rod 4 rods = chain CUBIC MEASURE,728 cu. inches = cu. foot 27 cu. feet = cu. yard 2,50.42 cu. inches = standard bushel cu. inches = standard gallon cu. foot = about 4/5 of a bushel 28 cu. feet = cord (wood) 40 cu. feet = ton (shipping) METRIC EQUIVALENT LINEAR MEASURE centimeter = inch decimeter = inches = foot meter = inches =.0936 yards dekameter =.9884 rods kilometer = mile inch = 2.54 centimeters foot = decimeters yard = meter rod = dekameter mile =.6093 kilometers SQUARE MEASURE sq. centimeter = sq. inches sq. inch = sq. centimeters sq. decimeter = sq. foot sq. foot = sq. decimeters sq. meter =.96 sq. yards sq. yard = sq. mile arc = sq. rod sq. rod = arc hektar = 2.47 acres acre = hektar sq. kilometer = sq. mile sq. mile = 2.59 sq. kilometers MEASURE OF VOLUME cu. centimeter = 0.06 cu. inch cu. inch = 6.39 cu. centimeters cu. decimeter = cu. foot cu. foot = cu. decimeters dekaliter = gallons gallon = dekaliter pk. = 0.88 dekaliter hektoliter = bu. bu. = hektoliter WEIGHTS gram = ounce ounce = grams kilogram = pounds pound = kilograms metric ton = 2,200 pounds or.023 English tons English ton = metric ton APPROXIMATE METRIC EQUIVALENTS decimeter = 4 inches meter =. yards liter =.06 qt. (liquid) or 0.9 qt. (dry) kilometer = 5/8 mile mile =.6 kilometers hektoliter = 2-5/8 bushels kilogram = 2-/5 pounds hektar = 2-/2 acres

4 CONVERSION TABLE MILLIMETERS AND FRACTIONS OF MILLIMETERS TO INCHES IN DECIMALS /00B = inches /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 =.002 5/50 =.08 6/50 = /50 = /50 =.047 9/50 = /50 = /50 = /50 = /50 =.08 24/50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = /50 = = = =.8 4 = = = = = = = = = =.58 4 = = = = = = = = = = = = = = = = =.80 3 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = millimeters = centimeter = inch 0 decimeters = meter = inches 0 centimeters = decimeter = inches 25.4 millimeters = inch DECIMAL CONVERSION TABLE EIGHTHS, SIXTEENTHS, THIRTY-SECONDS AND SIXTY-FOURTHS Eighths /8 =.25 /4 =.250 3/8 =.375 /2 =.500 5/8 =.625 3/4 =.750 7/8 =.875 Sixteenths /6 = /6 =.875 5/6 =.325 7/6 = /6 =.5625 /6 = /6 =.825 5/6 =.9375 Thirty-Seconds /32 = /32 = /32 = /32 = /32 =.2825 /32 = /32 = /32 = /32 = /32 = /32 = /32 = /32 = /32 = /32 = /32 = Sixty-Fourths /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 = /64 =

5 METRIC AND ENGLISH OR U.S. EQUIVALENT MEASURES MEASURES OF LENGTH meter = 39.3 inches feet.0936 yards centimeter =.3937 inch millimeter = inch, or ca. /25 inch kilometer = mile foot =.3048 meter inch = 2.54 centimeters 25.4 millimeters MEASURES OF WEIGHT gram = grains kilogram = pounds metric ton =.9842 ton of pounds 9.68 hundredweights 2,204.6 pounds grain = gram ounce avoirdupois = grams pound =.4536 kilogram ton of 2,240 pounds =.06 metric tons 06 kilograms MEASURES OF VOLUME AND CAPACITY cubic meter = cubic feet U.S. gallons (23 cu. in.).308 cubic yards cubic decimeter = cubic inches.0353 cubic feet cubic centimeter =.06 cubic inch liter = cubic decimeter cubic inches.0353 cubic foot.0567 quarts (U.S.).2642 gallon (U.S.) lbs. of water at 62º F. cubic yard =.7645 cubic meter cubic foot = cubic meter cubic decimeters liters cubic inch = cubic centimeters gallon (British) = liters gallon (U.S.) = liters MEASURES OF SURFACE square meter = square feet.96 square yards square centimeter =.55 square inch square millimeter =.0055 square inch square yard =.836 square meter square foot =.0929 square meter square inch = square centimeters square millimeters MISCELLANEOUS kilogram per meter =.6720 pounds per foot gram per square millimeter =.422 pounds per square inch kilogram per square meter = per square foot kilogram per cubic meter = per cubic foot degree centigrade =.8 degrees fahrenheit pound per foot =.4882 kilograms per meter

6 GEOMETRIC FORMULAE Area of a square = length x breadth or height Area of a rectangle = length x breadth or height Area of a triangle = base x /2 altitude Area of a parallelogram = base x altitude Area of a trapezoid = altitude x /2 the sum of parallel sides Area of a trapezium = divide into two triangles, total their areas Circumference of a circle = diameter x 3.46 Circumference of a circle = radius x Diameter of a circle = circumference x.383 Diameter of a circle = square root of area x.2838 Radius of a circle = circumference x Area of a circle = half diameter x half circumference Area of a circle = square of diameter x.7854 Area of a circle = square of circumference x Area of a sector of a circle = length of arc x /2 radius Area of a segment of a circle = area of sector of equal radius-area of triangle, when the segment is less, and plus area of triangle when segment is greater than the semi-circle Area or circular ring = sum of the diameter of the two circles x difference of the diameter of the two circles and that product x.7854 Side of a square that shall equal area of a circle = diameter x.8862 Side of a square that shall equal area of a circle = circumference x.282 Diameter of a circle that shall contain area of a given square = side of square x.284 Side of an inscribed equilateral triangle = diameter x.86 Side of an inscribed square = diameter x.707 Side of an inscribed square = circumference x.225 Area of an ellipse = product of the two diameters x.7854 Area of a parabola = base x 2/3 of altitude Area of a regular polygon = sum of its sides x perpendicular from its center to one of its sides divided by 2 Surface of a sphere = diameter x circumference Solidity of a sphere = surface x /6 diameter Solidity of a sphere = cube of diameter x.5236 Solidity of a sphere = cube of radius x Solidity of a sphere = cube of circumference x Diameter of a sphere = cube root of solidity x.2407 Diameter of a sphere = square root of surface x.5649 Circumference of a sphere = square root of surface x Circumference of a sphere = cube root of solidity x Contents of a segment of a sphere = (height squared plus three times the square of radius of base) x (height x.5236) Contents of a sphere = diameter x.5236 Side of an inscribed cube of a sphere = radius x.547 Side of an inscribed cube of a sphere = square root of diameter Surface of a pyramid or cone = circumference of base x /2 of the slant height plus area of base Contents of a pyramid or cone = area of base x /3 altitude Contents of frustrum of a pyramid or cone = sum of circumference at both ends x /2 slant height plus area of both ends Contents of frustrum of a pyramid or cone = multiply areas of two ends together and extract square root. Add to this root the two areas and x /3 altitude Contents of a wedge = area of base x /2 altitude

7 UNITS OF MEASUREMENT UNITS OF VOLUME AND WEIGHT Water in small tanks, cisterns and sumps is usually measured in gallons. Water in large tanks and small reservoirs is usually measured in cubic feet or gallons Water in large reservoirs is most commonly measured in acre-feet. Units U.S. Gallons Imperial Gallons Inches Feet Acre- Feet Pounds* Meters Liters U.S. Gallon = Imperial Gallon = Inch = Foot = Acre Foot = Pound = Meter = Liter = , , , , *Weights shown are based on maximum density of fresh water at 39º F. UNITS OF FLOW foot per second, also written second-foot, is the unit of flow in the English system used to express rate of flow in large pumps, ditches and canals. Flow in pipe lines, from pumps and wells is commonly measured in gallons per minute. Rates of water consumption and measurement of municipal water supply are ordinarily made in million gallons per day. The Miner s Inch is still used in some localities for irrigation and hydaulic mining, but not suitable for general use. Units U.S. Gallons/ Minute Million U.S. Gallons/ Day Feet/ Second Meters/ Hour Liter/ Second Miner s Inch As Set By State Laws I II III U.S. Gallon/Minute (U.S. G.P.M.) = Million U.S. Gallons/ Day (M.GD) = Foot/Second = Meter/Hour = Liter/Second = Miner s Inch (M.I.) I II III IV Ariz. Calif. Mont. Oreg. * Idaho Neb. Nev. N. Mex. Utah Kans. N. Dak. S. Dak. Colo. IV. A Miner s Inch legally set by British Columbia, 35.7 M.I. = Second-Foot *Usual practice in Southern California, 50 M.I. = Second-Foot = G.P.M.

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