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Area and volume: California D2 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. A round steel reservoir is 70 ft in diameter and 12 ft high. What is the surface area of the interior walls only (not the floor or roof)?

  1. A) 6,480 ft²
  2. B) 1,320 ft²
  3. C) 2,640 ft²
  4. D) 3,850 ft²
Show the answer and worked solution

Answer: C) 2,640 ft²

1. Circumference = 3.14 × D [Sheet p.1, Area and Volume: "Circumference of a Circle = 3.14 x D"] = 3.14 × 70 = 219.8 ft. 2. Wall area = circumference × height [Sheet p.1, Area and Volume: "Area of Rectangle = Length x Width"] = 219.8 × 12 = 2,637.6 ft². 3. Answer: 2,640 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"

Example 2. A cylindrical storage tank is 60 ft in diameter with water 33 ft deep. How many gallons does it hold?

  1. A) 11,600 gal
  2. B) 93,300 gal
  3. C) 698,000 gal
  4. D) 2,790,000 gal
Show the answer and worked solution

Answer: C) 698,000 gal

1. Cylinder Volume (Gal) = .785 × D² × Height × 7.48 [Sheet p.1, Area and Volume: "Cylinder Volume (Gal) = .785 x D2 x Height or Length (Ft) x 7.48"]. 2. = .785 × 60 × 60 × 33 × 7.48 = 697,570 gal. 3. Answer: 698,000 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. What is the cross-sectional area, in square feet, of a 21-inch diameter pipe?

  1. A) 346 ft²
  2. B) 1.37 ft²
  3. C) 2.40 ft²
  4. D) 9.62 ft²
Show the answer and worked solution

Answer: C) 2.40 ft²

1. Convert the diameter to feet: D = 21 in ÷ 12 in/ft = 1.75 ft [12 in = 1 ft]. 2. Area = .785 × D² [Sheet p.1, Area and Volume: "Area of Circle = .785 X D2"] = .785 × (21 ÷ 12)² = 2.404 ft². 3. Answer: 2.40 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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Practice all 174 area and volume problems for CA D2 Math

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