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
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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
1 Calculate the volume of the inside of the
container assigned to you and your
partner(s).
2 Calculate how many gallons of water the
container could theoretically hold.
• 1 cubic foot = 7.47 gallons of water*
3 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
• 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”
91”
inside
Inside
height
•5 Layers of Boxes High. (5 layers x 20 boxes)
•5 x 12.5” = 62.5 inches (possible 68”)
•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”)
Answer: 100 Boxes
(100 x 1.605 cu.ft. = 160.5 cu.ft.)
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
91”
height
inside
•5 Layers of Boxes High. (5 layers x 21 boxes)
•5 x 12.5” = 62.5 inches (possible 68”)
•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”)
•Answer: 105 Boxes
(105 x 1.605 cu.ft. = 168.525cu.ft.)
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)
6.031”
42”
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?
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
42”
•
= .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*
Volume = 1199.8224”³ divided by 231”³
= 5.1940 gal.
Industrial Applications:
Calculations: Volume of Pipe
3.042”
21.25”
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?
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)
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
2.049”
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?
Volume = πR²L or AL
61.375”
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)
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
47.125”
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)
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
47”
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)
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
37”
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)
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
46.375”
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)
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
51.375”
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)
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.