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### Industrial Skills

Volume: Descriptions, Calculations & Industrial Applications

Description: AreaA 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: VolumeA 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 20”

16” x 16” x 20” = 5,120 cu.in. divided by 1,728cu.in.

= 2.963 cubic feet

Inside Dimensions: 14” x 14” x 18”

14” x 14” x 18” = 3,528cu.in. ÷ 1,728cu.in.

= 2.042 cubic feet

2.042 cu.ft. x 7.47 gallons = 15.254 gallons of water

15.254 gal. x 8.34 pounds = 127.218 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 Cardboard Box: Outside – 12.5” x 12.5” x 17.75” 20 Boxes on bottom. (5 boxes long x 4 boxes wide) 5 Layers of Boxes High. (4 additional layers x 20 boxes) Answer: 100 Boxes(100 x 1.605 cu.ft. = 160.5 cu.ft.)

- ANSWER A:
- Trailer: Inside - 7ft.7in. by 4ft.9in. by 5ft.8in.
- 204.118 cubic feet

- 1.605 cubic feet

- 5 x 17.75” = 88.75 inches (possible 91”)
- 4 x 12.5” = 50 inches (possible 57”)

- 5 x 12.5” = 62.5 inches (possible 68”)

Container Question – Space UtilizationAnswer 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 Cardboard Box: Outside – 12.5” x 12.5” x 17.75” 21 Boxes on bottom. (7 boxes long x 3 boxes wide) 5 Layers of Boxes High. (4 additional layers x 21 boxes) Answer: 105 Boxes(105 x 1.605 cu.ft. = 168.525cu.ft.)

- ANSWER B:
- Trailer: Inside - 7ft.7in. by 4ft.9in. by 5ft.8in.
- 204.118 cubic feet

- 1.605 cubic feet

- 7 x 12.5” = 87.5 inches (possible 91”)
- 3 x 17.75” = 53.25 inches (possible 57”)

- 5 x 12.5” = 62.5 inches (possible 68”)

Container Question – Space UtilizationAnswer 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.

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