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Area and volume: California D3 water distribution 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. How many gallons does 900 ft of 18-inch water main hold?

  1. A) 5,950 gal
  2. B) 7,930 gal
  3. C) 1,590 gal
  4. D) 11,900 gal
Show the answer and worked solution

Answer: D) 11,900 gal

1. D = 18 ÷ 12 = 1.5 ft [12 in = 1 ft]. Keep (18 ÷ 12) in your calculator instead of the rounded value, so the answer is not thrown off. 2. Cylinder Volume (Gal) = .785 × D² × Length × 7.48 [Sheet p.1, Area and Volume: "Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48"]. 3. = .785 × (18 ÷ 12)² × 900 × 7.48 = 11,890 gal. 4. Answer: 11,900 gal (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48"

Example 2. How many gallons does 350 ft of 36-inch water main hold?

  1. A) 18,500 gal
  2. B) 6,170 gal
  3. C) 74,000 gal
  4. D) 2,470 gal
Show the answer and worked solution

Answer: A) 18,500 gal

1. D = 36 ÷ 12 = 3 ft [12 in = 1 ft]. 2. Cylinder Volume (Gal) = .785 × D² × Length × 7.48 [Sheet p.1, Area and Volume: "Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48"]. 3. = .785 × (36 ÷ 12)² × 350 × 7.48 = 18,496 gal. 4. Answer: 18,500 gal (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48"

Example 3. A round steel reservoir is 105 ft in diameter and 24 ft high. What is the surface area of the interior walls only (not the floor or roof)?

  1. A) 3,960 ft²
  2. B) 7,910 ft²
  3. C) 1,980 ft²
  4. D) 5,930 ft²
Show the answer and worked solution

Answer: B) 7,910 ft²

1. Circumference = 3.14 × D [Sheet p.1, Area and Volume: "Circumference of a Circle = 3.14 x D"] = 3.14 × 105 = 329.7 ft. 2. Wall area = circumference × height [Sheet p.1, Area and Volume: "Area of Rectangle = Length x Width"] = 329.7 × 24 = 7,912.8 ft². 3. Answer: 7,910 ft² (rounded to 3 significant figures).

Source: CA Exam Conversion Sheet (Revised 4/30/2026), p.1, Area and Volume: "Circumference of a Circle = 3.14 x D"; p.1, Area and Volume: "Area of Rectangle = Length x Width"

Want it on paper? Free printable D3 water distribution math worksheet with answer key.

Practice all 174 area and volume problems for CA D3 Math

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