Transcript Volume Calculations - Cape Fear Community College
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 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” inside 57” inside 91” inside 68” Inside height •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. (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.)
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” inside 57” inside 91” inside •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. (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.) 68” Inside height
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) 6.031” 42” What is the fluid volume of the pipe?
•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* Volume = 1199.8224
”³ divided by 231 ”³
= 5.1940 gal.
3.042”
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?
21.25” 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.
61.375” 2.049”
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?
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) 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.
47.125” 1.033”
Industrial Applications: Calculations:
Volume of Pipe 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) 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.
47” 0.810”
Industrial Applications: Calculations:
Volume of Pipe 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) 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.
37” 0.810”
Industrial Applications: Calculations:
Volume of Pipe 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) 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.
46.375” 0.528”
Industrial Applications: Calculations:
Volume of Pipe 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) 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.
51.375” 0.528”
Industrial Applications: Calculations:
Volume of Pipe 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) 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.