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Area and volume: California T1 water treatment operator math

Pipe, tank, basin, trench and wall areas and volumes; force on a valve.

Below are 3 worked examples. Each answer is computed with the formulas and constants on the CA Exam Conversion Sheet (revised 4/30/2026), and the solution names the line it uses.

Formulas from the sheet for this topic

Example 1. A rectangular basin is 105 ft long and 57 ft wide, with water 8.5 ft deep. How many gallons does it hold?

  1. A) 44,800 gal
  2. B) 424,000 gal
  3. C) 381,000 gal
  4. D) 50,900 gal
Show the answer and worked solution

Answer: C) 381,000 gal

1. Rectangular Basin (Gal) = L × W × H × 7.48 [Sheet p.1, Area and Volume: "Rectangular Basin (Gal) = Length (Ft) x Width (Ft) x Height (Ft) x 7.48"]. 2. = 105 × 57 × 8.5 × 7.48 = 380,526 gal. 3. Answer: 381,000 gal (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Rectangular Basin (Gal) = Length (Ft) x Width (Ft) x Height (Ft) x 7.48"

Example 2. A rectangular basin is 130 ft long and 54 ft wide, with water 16.5 ft deep. How many gallons does it hold?

  1. A) 52,500 gal
  2. B) 866,000 gal
  3. C) 116,000 gal
  4. D) 966,000 gal
Show the answer and worked solution

Answer: B) 866,000 gal

1. Rectangular Basin (Gal) = L × W × H × 7.48 [Sheet p.1, Area and Volume: "Rectangular Basin (Gal) = Length (Ft) x Width (Ft) x Height (Ft) x 7.48"]. 2. = 130 × 54 × 16.5 × 7.48 = 866,408 gal. 3. Answer: 866,000 gal (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Rectangular Basin (Gal) = Length (Ft) x Width (Ft) x Height (Ft) x 7.48"

Example 3. What is the cross-sectional area, in square feet, of a 27-inch diameter pipe?

  1. A) 1.77 ft²
  2. B) 15.9 ft²
  3. C) 572 ft²
  4. D) 3.97 ft²
Show the answer and worked solution

Answer: D) 3.97 ft²

1. Convert the diameter to feet: D = 27 in ÷ 12 in/ft = 2.25 ft [12 in = 1 ft]. 2. Area = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (27 ÷ 12)² = 3.974 ft². 3. Answer: 3.97 ft² (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Area of Circle = .785 X D2"

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