Volume of a cylinder worksheet: practice problems with answers
This volume of a cylinder worksheet has 15 practice problems, graded from basic radius-and-height questions to unit conversions, reverse problems and word problems. Each uses V = πr²h, and each has a worked answer folded underneath so you can try it first. All answers use the full value of π, rounded at the end.
Contents
V = π × r² × h. With r = 4 in and h = 9 in: π × 16 × 9 = 144π ≈ 452.39 in³.
Use the calculator above to check your answers: enter the radius (or switch to the diameter) and the height, and compare the volume and the steps. If you need a refresher first, the guide on how to find the volume of a cylinder explains the method with worked examples.
Before you start
- Formula: V = πr²h. With a diameter, r = d ÷ 2, or use V = πd²h ÷ 4.
- Units: both measurements in the same unit. The answer is in cubic units.
- Conversions: 1 ft = 12 in, 1 ft³ = 1,728 in³, 1 US gal = 231 in³, 1 ft³ ≈ 7.48052 US gal, 1 yd³ = 27 ft³, 1 L = 1,000 cm³, 1 m³ = 1,000 L.
- Rounding: two decimal places unless the problem says otherwise.
Level 1: basic cylinder volume questions
Problem 1
A cylinder has a radius of 4 in and a height of 9 in. Find its volume.
Show the answer
r² = 16. Base area = π × 16 ≈ 50.27 in². V = 16π × 9 = 144π ≈ 452.39 in³.
Problem 2
A cylinder has a diameter of 10 cm and a height of 12 cm. Find its volume.
Show the answer
The radius is 10 ÷ 2 = 5 cm, so r² = 25. V = π × 25 × 12 = 300π ≈ 942.48 cm³. Using 10 as the radius would give 3,769.91 cm³, four times too much.
Problem 3
Find the volume of a cylinder with a radius of 2.5 m and a height of 4 m.
Show the answer
r² = 6.25. V = π × 6.25 × 4 = 25π ≈ 78.54 m³.
Problem 4
A cylinder has a radius of 6 ft and a height of 10 ft. Give the volume in terms of π, then as a decimal.
Show the answer
V = π × 36 × 10 = 360π ft³ ≈ 1,130.97 ft³.
Level 2: units and conversions
Problem 5
A vase is 8 in wide and 2 ft tall inside. How many cubic inches does it hold? How many US gallons?
Show the answer
Convert the height: 2 ft = 24 in. The radius is 4 in. V = π × 16 × 24 = 384π ≈ 1,206.37 in³. In gallons: 1,206.37 ÷ 231 ≈ 5.22 US gal.
Problem 6
A water tank is 3 ft across and 5 ft tall. How many US gallons does it hold when full?
Show the answer
r = 1.5 ft, r² = 2.25. V = π × 2.25 × 5 = 11.25π ≈ 35.34 ft³. In gallons: 35.343 × 7.48052 ≈ 264.38 US gal.
Problem 7
A can has an inside diameter of 7.5 cm and an inside height of 11 cm. How many milliliters does it hold?
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r = 3.75 cm, r² = 14.0625. V = π × 14.0625 × 11 ≈ 485.97 cm³. Since 1 cm³ = 1 mL, the can holds about 486 mL.
Problem 8
A pipe has an inside diameter of 40 mm and is 25 m long. How many liters of water fill it?
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Work in meters: r = 20 mm = 0.02 m, r² = 0.0004. V = π × 0.0004 × 25 = 0.01π ≈ 0.031416 m³. One cubic meter is 1,000 L, so the pipe holds about 31.42 L. The pipe volume calculator gives the same figure per foot or per meter.
Level 3: reverse problems (find the height or the radius)
Problem 9
A cylinder holds 1,000 cm³ and has a radius of 5 cm. How tall is it?
Show the answer
h = V ÷ (πr²) = 1,000 ÷ (π × 25) = 1,000 ÷ 78.54 ≈ 12.73 cm. The method is explained on the page about how to find the height of a cylinder.
Problem 10
A cylinder has a volume of 500 in³ and a height of 10 in. Find its radius.
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r² = V ÷ (πh) = 500 ÷ (π × 10) ≈ 15.915. r = √15.915 ≈ 3.99 in. Do not stop at r²: the square root is part of the answer. See how to find the radius of a cylinder for more cases.
Problem 11
A tank 20 in across must hold 50 US gallons. How tall must it be inside?
Show the answer
Convert the volume: 50 × 231 = 11,550 in³. r = 10 in, so the base area is π × 100 ≈ 314.16 in². h = 11,550 ÷ 314.16 ≈ 36.76 in.
Level 4: volume of a cylinder word problems
Problem 12: concrete columns
You pour 4 round columns, each 12 in across and 4 ft deep. How much concrete do you need in cubic feet and cubic yards? How many 80 lb bags, if the bag says one bag yields about 0.60 ft³?
Show the answer
r = 6 in = 0.5 ft. One column: π × 0.25 × 4 = π ≈ 3.14 ft³. Four columns: 4π ≈ 12.57 ft³. In cubic yards: 12.566 ÷ 27 ≈ 0.47 yd³. Bags: 12.566 ÷ 0.60 ≈ 20.94, so 21 bags, before any extra for waste. The concrete calculator for round forms adds a waste margin.
Problem 13: a round pool
An above-ground pool is 15 ft across and filled to a depth of 4 ft. How many US gallons of water are in it?
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r = 7.5 ft, r² = 56.25. V = π × 56.25 × 4 = 225π ≈ 706.86 ft³. In gallons: 706.86 × 7.48052 ≈ 5,287.67 US gal, about 5,290 gallons.
Problem 14: filling glasses
A glass has an inside radius of 3.5 cm and is filled to a height of 12 cm. How many full glasses can you pour from a 2 L bottle?
Show the answer
One glass: π × 12.25 × 12 = 147π ≈ 461.81 cm³. The bottle holds 2,000 cm³. 2,000 ÷ 461.81 ≈ 4.33, so 4 full glasses, with about 152.74 cm³ (153 mL) left over.
Problem 15: changing the dimensions
Cylinder A has a radius of 3 in and a height of 10 in. Cylinder B has twice the radius and half the height. Which holds more, and by how much?
Show the answer
A: π × 9 × 10 = 90π ≈ 282.74 in³. B: r = 6 in, h = 5 in, so π × 36 × 5 = 180π ≈ 565.49 in³. B holds twice as much. Doubling the radius multiplies the volume by 4, halving the height divides it by 2: 4 ÷ 2 = 2.
Answer key
| Problem | Answer | Problem | Answer |
|---|---|---|---|
| 1 | 452.39 in³ | 9 | 12.73 cm |
| 2 | 942.48 cm³ | 10 | 3.99 in |
| 3 | 78.54 m³ | 11 | 36.76 in |
| 4 | 360π ≈ 1,130.97 ft³ | 12 | 12.57 ft³, 0.47 yd³, 21 bags |
| 5 | 1,206.37 in³, 5.22 US gal | 13 | 5,287.67 US gal |
| 6 | 264.38 US gal | 14 | 4 glasses |
| 7 | 486 mL | 15 | B, twice as much |
| 8 | 31.42 L |
How to solve cylinder word problems
- Find what is askedVolume, capacity in gallons or liters, a height, a radius, a number of containers.
- List the measurementsWrite each with its unit. Mark whether you have a radius or a diameter.
- Convert to one unitPick the unit closest to the answer you need: feet for gallons via 7.48052, inches for gallons via 231, centimeters for liters.
- Apply the formulaV = πr²h forward; h = V ÷ πr² or r = √(V ÷ πh) for reverse problems.
- Convert and roundRound once, at the end, then check that the answer is reasonable.
Quick check: a cylinder fills π ÷ 4, about 78.5 %, of the box around it. In problem 1, the box is 8 × 8 × 9 = 576 in³, and 452.39 is 78.5 % of 576. If your answer is larger than the box, you used the diameter as the radius.
Cylinders in real life
Most word problems use objects you can measure at home: cans, glasses, candles, jars, rolling pins, round cake pans, buckets with straight sides, batteries. Outdoors and on building sites, you meet them as water tanks, rain barrels, pipes, culverts, round columns and silos. For each, the volume formula answers "how much does it hold?" when you use inside dimensions, and "how much material is it?" when you use outside dimensions. A tube or a pipe wall needs the hollow cylinder volume formula instead.
Many worksheets mix volume with surface area questions, which ask for the material on the outside in square units: A = 2πr² + 2πrh. The method and worked examples are on the page about the surface area of a cylinder. Worksheets on cones and spheres reuse the same radius and height; the page comparing the volume of a cylinder, cone and sphere shows how their formulas relate. To check any answer quickly, use the cylinder volume calculator.
FAQ
How do you solve volume of a cylinder word problems?
Underline what the question asks (volume, height, radius, gallons), list the measurements with their units, convert them to one unit, then apply V = πr²h or its rearranged form. Finish by converting the answer to the unit asked for and checking that it is reasonable.
Should answers be left in terms of π?
Only when the question says so. An exact answer such as 144π in³ keeps full precision; a decimal answer such as 452.39 in³ is what most real-life questions expect. Use the π key and round at the end.
What are real-life examples of cylinders?
Cans, glasses, candles, water tanks, pipes, drums, round pillars, silos, rolling pins and batteries are all close to cylinders. For each, V = πr²h gives how much it holds, using inside dimensions.
How do I check my answers to cylinder volume questions?
Enter the radius or diameter and the height in the calculator on this page and compare. A quick sanity check: the volume must be about 78.5 % of the box (2r) × (2r) × h that fits around the cylinder.
What is the most common mistake on a volume of a cylinder worksheet?
Using the diameter as the radius, which makes the answer four times too big. The second is mixing units, such as a radius in inches with a height in feet.
Related
- How to find the volumeHow to find the volume of a cylinder: square the radius, multiply by π and the height. Worked examples in inches, feet, cm and m, plus common mistakes.
- Height of a cylinderHow to find the height of a cylinder: h = V ÷ (πr²) from the volume, or from the surface area. Calculator, tank examples in gallons and liters, common traps.
- Radius of a cylinderHow to find the radius of a cylinder from its volume, surface area, circumference or diameter. Formulas, calculator and worked examples in inches and cm.
Updated October 12, 2026