Volume: Descriptions, Calculations & Industrial Applications Industrial Skills Volume: Descriptions, Calculations & Industrial Applications

Description: Area A Two-Dimensional Quantity Area measurements utilize linear measurements to calculate the number of unit squares within a given boundary. Measurements of area are expressed in “square units” such as square inches, square feet, square meters, etc. They have length and width but thickness is not considered in the calculations. Never mix units in the same calculation.

Description: Volume A Three-Dimensional Quantity Volume is the space an object occupies or the capacity of a container. Volume calculations combine three measurements: usually length, height, and depth or thickness. Volume is always expressed in “cubic units” such as cubic inches, cubic feet, cubic meters, etc. A variety of different volume formulas may be used, depending on the shape of the object. Check your handout for exact formulas. Never mix units in the same calculation.

Industrial Applications: Common Quantities and Conversions 1 square foot = 144 square inches 1 square yard = 9 square feet = 1,296 sq. in. 1 cubic foot = 1,728 cubic inches 1 cubic yard = 27 cubic feet = 46,656 cu. in. 1 cubic foot = 7.47 gallons of water* 1 gallon of water = 8.3453 pounds* 1 square centimeter = 100 square millimeters 1 square meter =10,000 sq.cm.=1,000,000 sq.mm 1 cubic meter = 1,000,000,000 cubic millimeters 1 cubic meter = 1,000 liters of water* 1 cubic meter = 264.2 gallons of water* 1 liter of water = 1.000 Kilogram*

Industrial Applications: Container Questions – Gallons & Weight Calculate the volume of the inside of the container assigned to you and your partner(s). Calculate how many gallons of water the container could theoretically hold. 1 cubic foot = 7.47 gallons of water* Calculate how much the water in the container would weigh. 1 gallon of water = 8.3453 pounds*

Industrial Applications: Calculations Scrap Rope Box: Outside Dimensions: 36” x 32” x 18” 36” x 32” x 18” = 20,736 cu.in. divided by 1,728cu.in. = 12 cubic feet Inside Dimensions: 33¾” x 29¾” x 15¾” 33.75” x 29.75” x 15.75” = 15,813.984cu.in. ÷ 1,728cu.in. = 9.152 cubic feet 9.152 cu.ft. x 7.47 gallons = 68.365 gallons of water 68.365 gal. x 8.34 pounds = 570.164 pounds

Other Calculations: Box A: Wood Box with Handles Outside Dimensions: 12” x 16” x 32” 12” x 16” x 32” = 6,144 cu.in. divided by 1,728cu.in. = 3.556 cubic feet Inside Dimensions: 9¾” x 13¾” x 29¾” 9.75” x 13.75” x 29.75” = 3,988.359cu.in. ÷ 1,728cu.in. = 2.308 cubic feet 2.308 cu.ft. x 7.47 gallons = 17.241 gallons of water 17.241 gal. x 8.34 pounds = 143.790 pounds

Other Calculations: Box B: Small Wood Box Outside Dimensions: 16” x 16” x 18¼” 16” x 16” x 18.25” = 4,672 cu.in. divided by 1,728cu.in. = 2.704 cubic feet Inside Dimensions: 14” x 14” x 16½” 14” x 14” x 16. 5” = 3,234cu.in. ÷ 1,728cu.in. = 1.872 cubic feet 1.872 cu.ft. x 7.47 gallons = 13.984 gallons of water 13.984 gal. x 8.34 pounds = 116.627 pounds

Other Calculations: Box C: “Grainger” Cardboard Box Outside Dimensions: 12½” x 12½” x 17¾” 12.5” x 12.5” x 17.75” = 2885.484 cu.in. divided by 1,728cu.in. = 1.670 cubic feet Inside Dimensions: 12¼” x 12¼” x 17½” 12.25” x 12.25” x 17.5” = 2,626.094 cu.in. ÷ 1,728cu.in. = 1.5197 cubic feet 1.520 cu.ft. x 7.47 gallons = 11.354 gallons of water 11.354 gal. x 8.34 pounds = 94.692 pounds

Other Calculations: Box D: Plain Cardboard Box Outside Dimensions: 15¼” x 15¼” x 15¼” 15.25” x 15.25” x 15.25” = 3546.578 cu.in. divided by 1,728cu.in. = 2.052 cubic feet Inside Dimensions: 15” x 15” x 15” 15” x 15” x 15” = 3,375 cu.in. ÷ 1,728cu.in. = 1.953 cubic feet 1.953 cu.ft. x 7.47 gallons = 14.589 gallons of water 14.589 gal. x 8.34 pounds = 121.672 pounds

Other Calculations: Stackable Fish Box: Inside Dimensions (Rough): 11¼” x 16¾” x 29¾” 11.25” x 16.75” x 29.75” = 5606.016 cu.in. divided by 1,728cu.in. = 3.244 cubic feet Subtract a total of .248 cu. ft. True Inside Volume* = 2.996 cubic feet 2.996 cu.ft. x 7.47 gallons = 22.380 gallons of water 22.380 gal. x 8.34 pounds = 186.649 pounds

Industrial Applications: Volume Question – Sea Salt Dilution Calculate how much “synthetic sea salt” should be added to the water in “fish box” container. The mixing instructions stipulate: 7 pounds of Coralife Scientific Grade Marine Salt to 25 gallons of water. Fish Box: Volume*: 2.996 cu.ft. Volume of Water: 22.380 gallons

Industrial Applications: Volume Question – Sea Salt Dilution 7 pounds of “Salt” to 25 gallons of water. Fish Box: Volume*: 2.996 cu.ft. Volume of Water: 22.380 gallons 7 pounds = 112 ounces (7 x 16 ounces per pound) 112 oz. divided by 25 gal. = 4.48 oz. of salt per gallon of water 22.380 gal. x 4.48 oz. = 100.2624 oz. of salt 100.2624 divided by 16 oz. = 6.2664 pounds of salt

Industrial Applications: Container Question – Space Utilization A 5’x 8’ trailer has interior dimensions of 7ft.7in. long by 4ft.9in. wide by 5ft.8in. high. How many of the cardboard boxes shown earlier could we pack into the trailer? Cardboard Box: Outside – 12.5” x 12.5” x 17.75”

Industrial Applications: Container Question – Space Utilization ANSWER A: Trailer: Inside - 7ft.7in. by 4ft.9in. by 5ft.8in. 204.118 cubic feet Cardboard Box: Outside – 12.5” x 12.5” x 17.75” 1.605 cubic feet 20 Boxes on bottom. (5 boxes long x 4 boxes wide) 5 x 17.75” = 88.75 inches (possible 91”) 4 x 12.5” = 50 inches (possible 57”) 5 Layers of Boxes High. (4 additional layers x 20 boxes) 5 x 12.5” = 62.5 inches (possible 68”) Answer: 100 Boxes (100 x 1.605 cu.ft. = 160.5 cu.ft.)

Container Question – Space Utilization Answer A: 57” 57” inside inside 68” Inside height 91” inside 5 Layers of Boxes High. (5 layers x 20 boxes) 5 x 12.5” = 62.5 inches (possible 68”) Answer: 100 Boxes (100 x 1.605 cu.ft. = 160.5 cu.ft.) 20 Boxes on bottom. (5 boxes long x 4 boxes wide) 5 x 17.75” = 88.75 inches (possible 91”) 4 x 12.5” = 50 inches (possible 57”)

Industrial Applications: Container Question – Space Utilization ANSWER B: Trailer: Inside - 7ft.7in. by 4ft.9in. by 5ft.8in. 204.118 cubic feet Cardboard Box: Outside – 12.5” x 12.5” x 17.75” 1.605 cubic feet 21 Boxes on bottom. (7 boxes long x 3 boxes wide) 7 x 12.5” = 87.5 inches (possible 91”) 3 x 17.75” = 53.25 inches (possible 57”) 5 Layers of Boxes High. (4 additional layers x 21 boxes) 5 x 12.5” = 62.5 inches (possible 68”) Answer: 105 Boxes (105 x 1.605 cu.ft. = 168.525cu.ft.)

Container Question – Space Utilization Answer B: 57” 57” inside inside 68” Inside height 91” inside 5 Layers of Boxes High. (5 layers x 21 boxes) 5 x 12.5” = 62.5 inches (possible 68”) Answer: 105 Boxes (105 x 1.605 cu.ft. = 168.525cu.ft.) 21 Boxes on bottom. (7 boxes long x 3 boxes wide) 7 x 12.5” = 87.5 inches (possible 91”) 3 x 17.75” = 53.25 inches (possible 57”)

Industrial Applications: Calculations: Volume of Cylinders (Pipe) Volume = πR²L or AL Volume is always expressed in cubic units. 6.031” 6.625”

Industrial Applications: Calculations: Volume of Cylinders (Pipe) A section of the 6 inch clear PVC pipe used for the preservation of a large fish specimen is 42 inches long. What is the volume of the pipe? 6.031” 42” Volume = πR²L or AL *Always square radius first 6.031” Diameter = 3.0155” Radius (6.031”/2) Area = πR² = π x 3.0155” ² = π x 9.0932” = 3.1416 x 9.0932” = 28.5672 sq.in. Volume = πR²L = 28.5672” ² x 42” length = 1199.8224 cubic inches 1199.8224”³ / 1728 ”³ = .6943 cubic feet

Industrial Applications: Calculations: Volume of Cylinders (Pipe) What is the fluid volume of the pipe? 6.031” Volume = 1199.8224 ”³ = .6943 cubic feet 1 cubic foot = 7.47 gallons of water* 1 gallon of water = 231cu.in. (1728 ”³/7.47gal.) 1 gallon of water = 8.3453 pounds* 42” Volume = 1199.8224”³ divided by 231”³ = 5.1940 gal.

Industrial Applications: Calculations: Volume of Pipe A section of white 3 inch PVC pipe is 20¾ inches long. With the cap on one end the inside distance of the pipe is actually 21¼ in. What is the solid and the fluid volume (water) of this pipe? 3.042” Volume = πR²L or AL 3.042” Diameter = 1.521” Radius (3.042”/2) Area = πR² = π x 1.521” ² = π x 2.3134” = 3.1416 x 2.3134” = 7.2679 sq.in. Volume = πR²L = 7.2679” ² x 21.25” length = 154.4427 cubic inches (solid volume) 154.4427”³ / 1728 ”³ = .08938 cubic feet (solid volume) 21.25” Fluid Volume: 154.4427”³ divided by 231”³ = .66858 gal. or .08938 cubic feet x 7.47 gal. = .66767 gal. Which can then be converted to fluid ounces by: .66767 x 128oz. = 85.46 fl. oz.

Industrial Applications: Calculations: Volume of Pipe A section of white 2 inch PVC pipe is 61.375 in. long. What is the solid and the fluid volume (water) of this pipe? 2.049” Volume = πR²L or AL 2.049” Diameter = 1.0245” Radius (2.049”/2) Area = πR² = π x 1.0245”² = π x 1.0496” = 3.1416 x 1.0496” = 3.2974 sq.in. Volume = πR²L = 3.2974” ² x 61.375” length = 202.3779 cubic inches (solid volume) 202.3779”³ / 1728 ”³ = .11712 cubic feet (solid volume) 61.375” Fluid Volume: 202.3779”³ divided by 231”³ = .87610 gal. or .11712 cubic feet x 7.47 gal. = .87489 gal. Which can then be converted to fluid ounces by: .87489 x 128oz. = 111.99 fl. oz.

Industrial Applications: Calculations: Volume of Pipe 1.033” A section of white 1 inch PVC pipe is 47.125 in. long. What is the solid and the fluid volume (water) of this pipe? Volume = πR²L or AL 1.033” Diameter = 0.5165” Radius (1.033”/2) Area = πR² = π x 0.5165”² = π x 0.26677” = 3.1416 x 0.26677” = 0.83808 sq.in. Volume = πR²L = .83808”² x 47.125” length = 39.49452 cubic inches (solid volume) 39.49452”³ / 1728 ”³ = .022856 cubic feet (solid volume) 47.125” Fluid Volume: 39.49452”³ divided by 231”³ = .17097 gal. or .022856 cubic feet x 7.47 gal. = .17073 gal. Which can then be converted to fluid ounces by: .17073 x 128oz. = 21.85 fl. oz.

Industrial Applications: Calculations: Volume of Pipe 0.810” A section of white ¾ inch PVC pipe is 47in. long. What is the solid and the fluid volume (water) of this pipe? Volume = πR²L or AL 0.810” Diameter = 0.405” Radius (.810”/2) Area = πR² = π x 0.405”² = π x 0.164025” = 3.1416 x 0.164025” = 0.515300 sq.in. Volume = πR²L = .515300”² x 47.0” length = 24.2191 cubic inches (solid volume) 24.2191”³ / 1728 ”³ = .01402 cubic feet (solid volume) 47” Fluid Volume: 24.2191”³ divided by 231”³ = .10485 gal. or .01402 cubic feet x 7.47 gal. = .10473 gal. Which can then be converted to fluid ounces by: .10473 x 128oz. = 13.41 fl. oz.

Industrial Applications: Calculations: Volume of Pipe 0.810” A section of white ¾ inch PVC pipe is 37in. long. What is the solid and the fluid volume (water) of this pipe? Volume = πR²L or AL 0.810” Diameter = 0.405” Radius (.810”/2) Area = πR² = π x 0.405”² = π x 0.164025” = 3.1416 x 0.164025” = 0.515300 sq.in. Volume = πR²L = .515300”² x 37.0” length = 19.0661 cubic inches (solid volume) 19.0661”³ / 1728 ”³ = .01103 cubic feet (solid volume) 37” Fluid Volume: 19.0661”³ divided by 231”³ = .08254 gal. or .01103 cubic feet x 7.47 gal. = .08239 gal. Which can then be converted to fluid ounces by: .08239 x 128oz. = 10.55 fl. oz.

Industrial Applications: Calculations: Volume of Pipe 0.528” A section of gray, schedule 80 - ½ inch PVC pipe is 46.375in. long. What is the solid and the fluid volume (water) of this pipe? Volume = πR²L or AL 0.528” Diameter = 0.264” Radius (.528”/2) Area = πR² = π x 0.264”² = π x 0.069696” = 3.1416 x 0.069696” = 0.21896 sq.in. Volume = πR²L = .21896”² x 46.375” length = 10.15427 cubic inches (solid volume) 10.15427”³ / 1728 ”³ = .00588 cubic feet (solid volume) 46.375” Fluid Volume: 10.15427”³ divided by 231”³ = .04396 gal. or .00588 cubic feet x 7.47 gal. = .04392 gal. Which can then be converted to fluid ounces by: .04392 x 128oz. = 5.62 fl. oz.

Industrial Applications: Calculations: Volume of Pipe 0.528” A section of gray, schedule 80 - ½ inch PVC pipe is 51.375in. long. What is the solid and the fluid volume (water) of this pipe? Volume = πR²L or AL 0.528” Diameter = 0.264” Radius (.528”/2) Area = πR² = π x 0.264”² = π x 0.069696” = 3.1416 x 0.069696” = 0.21896 sq.in. Volume = πR²L = .21896”² x 51.375” length = 11.24907 cubic inches (solid volume) 11.24907”³ / 1728 ”³ = .00651 cubic feet (solid volume) 51.375” Fluid Volume: 11.24907”³ divided by 231”³ = .048698 gal. or .00651 cubic feet x 7.47 gal. = .048630 gal. Which can then be converted to fluid ounces by: .048630 x 128oz. = 6.23 fl. oz.