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Zorluk: Çok zorUS Customary Capacity and Volume

A chemical processing plant uses a rectangular holding tank measuring 44 feet long, 33 feet wide, and 22 feet deep. The tank is currently filled to exactly 25%25\% of its total capacity with an industrial solvent. The plant manager needs to transfer all of this solvent into small safety bottles that each hold 1515 fluid ounces. Given that 11 cubic foot holds exactly 7.57.5 gallons, and 11 gallon contains 128128 fluid ounces, what is the maximum number of completely full safety bottles that can be filled from the tank?

  1. A
    144
  2. B
    192
  3. 384Cevap
  4. D
    1536

Cevap

384
The correct answer is found by first calculating the actual volume of solvent in the tank (66 cubic feet), converting this volume sequentially through gallons into fluid ounces (57605760 fluid ounces), and finally dividing by the per-bottle capacity (1515 fluid ounces).

Adım Adım Çözüm

1
Calculate the total capacity of the rectangular tank.
2424 cubic feet
The volume of a rectangular prism is found by multiplying length ×\times width ×\times depth (4×3×24 \times 3 \times 2).
2
Determine the actual volume of the solvent currently in the tank.
66 cubic feet
The tank is only 25%25\% full, so we calculate 0.25×240.25 \times 24.
3
Convert the solvent volume from cubic feet to gallons.
4545 gallons
Using the provided conversion factor, multiply the cubic feet by the gallons per cubic foot (6×7.56 \times 7.5).
4
Convert the solvent volume from gallons to fluid ounces.
57605760 fluid ounces
Using the standard conversion factor, multiply the gallons by the fluid ounces per gallon (45×12845 \times 128).
5
Calculate the number of completely full bottles.
384384 bottles
Divide the total available fluid ounces by the capacity of a single bottle (5760÷155760 \div 15).

Anahtar Kavram

Multi-step volume and capacity conversions incorporating dimensional calculations and partial quantities.
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Konular

US Customary Capacity and Volume

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