The formula of volume of cylinder is V = πr²h. Find the area of the circle at the end, πr², then multiply by the height, h. Here r is the radius, half the width across.
A cylinder is a stack of equal circles.
V = πr² × h
Hello, curious mind!
What is the volume of a cylinder?
The volume of a cylinder is the space inside it: the area of its circle end times its height, V = πr²h.
Think of a stack of coins. Each coin is a thin circle with area πr². More coins make a taller stack. So volume = circle area × height.
r² means r × r (see exponents). π is about 3.14159. Keep π, or use the π key, until the last step.
What happens when r or h changes
| Change | New volume | Why |
|---|---|---|
| Double the height | 2 times | h is not squared |
| Double the radius | 4 times | 2² = 4 |
| Triple the radius | 9 times | 3² = 9 |
| Double r, halve h | 2 times | 4 × ½ = 2 |
Remember this
Given the width across? Halve it first.
How to use the formula of volume of cylinder: 3 worked examples
Example 1: find the volume of a candle
A candle is 10 cm across and 12 cm tall.
The diameter is 10 cm, so r = 5 cm.
V = π × 5² × 12 = π × 25 × 12 = 300π.
V ≈ 942.5 cm³.
Example 2: find the height from the volume
A tin holds 1,000 cm³ and has a radius of 5 cm. How tall is it?
Turn the formula round: h = V ÷ (πr²).
πr² = 25π ≈ 78.54 cm².
h = 1,000 ÷ 78.54 ≈ 12.7 cm.
To find r, divide V by πh, then take the square root. If V = 392π cm³ and h = 8 cm, then r² = 392 ÷ 8 = 49, so r = 7 cm.
Example 3: a hollow pipe
A pipe is 200 cm long. Its outer radius is 5 cm and its inner radius is 4 cm. How much metal is in it?
Take the hole away from the full cylinder: V = π(R² − r²)h.
V = π × (25 − 16) × 200 = 1,800π.
V ≈ 5,654.9 cm³.
π(5 − 4)² × 200 = 200π is far too small. Square each radius first, then subtract.
Units and litres
Volume is in cubic units, such as cm³ or m³. For litres:
- 1 cm³ = 1 mL, so 1,000 cm³ = 1 L.
- 1 m³ = 100 × 100 × 100 = 1,000,000 cm³ = 1,000 L.
So a litre is not 1 m³. That mix-up is common on maths help forums, and it makes an answer 1,000 times wrong.
A rooftop water tank in Dubai (made-up numbers)
A round tank has a radius of 0.6 m and a height of 1.5 m.
V = π × 0.6² × 1.5 = 0.54π ≈ 1.6965 m³.
× 1,000: the tank holds about 1,696 litres when full.
A drinks can (made-up numbers)
A can 6 cm across and 12 cm tall: V = π × 3² × 12 = 108π ≈ 339.3 cm³, so about 339 mL.
Bonus: the longest straight straw that fits in a shorter can, 6 cm across and 8 cm tall, is 10 cm. It runs from a bottom edge to the far top edge. That uses Pythagoras’ theorem: 6² + 8² = 10².
Common volume of a cylinder mistakes
- Using the diameter as the radius. For the candle, π × 10² × 12 = 1,200π. That is 4 times too big.
- Squaring the height. π × 5 × 12² = 720π. Only r is squared.
- Mixing cm and m. A tank with r = 50 cm and h = 2 m is not π × 50² × 2. Use r = 0.5 m: V = 0.5π ≈ 1.571 m³, about 1,571 L.
- Rounding π too early. For r = 9 cm and h = 20 cm, π × 81 ≈ 254.47. Rounding that to 254 gives 5,080 cm³. The true answer is about 5,089.4 cm³.
- Leaving out units. “339” alone could mean cm³, mL or m³. Write the unit every time.
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- Uses the diameter as the radius: DRC, did not read carefully.
- Squares the height instead of the radius: CNC, concept not clear.
- Mixes cm and m in one sum: CWV, copied a wrong value.
- Rounds π too early, so the answer is off: CMT, calculation mistake.
- Leaves out units: BPT, bad presentation.
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Test prep corner
Cylinder volume in SAT maths
College Board lists “Area and volume” in SAT Geometry and Trigonometry. The reference sheet in College Board’s digital SAT practice tests gives V = πr²h. So the SAT tests whether you can use it, not whether you remember it. These are SAT-style practice questions, not real past questions.
SAT-style: Cylinder A has radius 3 and height 10. Cylinder B has twice the radius and half the height. The volume of B is how many times the volume of A? (A) 1 (B) 2 (C) 4 (D) 8
A: π × 9 × 10 = 90π. B: π × 36 × 5 = 180π. So B is 2 times A, answer (B). Fast way: 2² × ½ = 2. Trap: (C), from doubling r and forgetting the height.
SAT-style: A full cylinder of water has radius 6 cm and height 10 cm. All of it is poured into an empty cylinder of radius 4 cm. How high, in cm, does the water reach?
The volume stays the same: π × 36 × 10 = 360π. In the new cylinder, π × 16 × h = 360π, so h = 360 ÷ 16 = 22.5. Trap: 10 × 6 ÷ 4 = 15, which forgets to square the radii.
Practise more with our SAT-style maths practice questions.
Facts checked on 11 November 2026 on satsuite.collegeboard.org.
Quick check: 5 volume of a cylinder questions
1. A cylinder has r = 2 cm and h = 5 cm. What is its volume?
Yes! π × 4 × 5 = 20π.
Not quite. Square the radius, not the height.
Not quite. Square the radius: 2² = 4.
2. A cylinder is 8 cm across and 3 cm tall. What is its volume?
Not quite. 8 cm is the diameter. Halve it.
Yes! r = 4, so π × 16 × 3 = 48π.
Not quite. Halve 8, then square it.
3. V = 98π cm³ and r = 7 cm. What is h?
Not quite. Divide by 7², not 7.
Not quite. 49 is r². Divide 98 by it.
Yes! h = 98 ÷ 49 = 2.
4. How many litres is 2,500 cm³?
Yes! 2,500 ÷ 1,000 = 2.5.
Not quite. Divide by 1,000, not 100.
Not quite. 1,000 cm³ is 1 L.
5. You triple the radius and keep the height. The volume becomes how many times bigger?
Not quite. The radius is squared.
Not quite. Square 3, do not double it.
Yes! 3² = 9.
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Questions people ask about the volume of a cylinder
What is the formula of volume of cylinder?
V = πr²h, where r is the radius of the circle end and h is the height. It is the circle area times the height.
How do I find the height from the volume?
Divide the volume by πr². For example, 1,000 cm³ ÷ (π × 5²) ≈ 12.7 cm.
How do I change cm³ to litres?
Divide by 1,000, as 1,000 cm³ = 1 L. For m³, multiply by 1,000, as 1 m³ = 1,000 L.
What is the volume of a hollow cylinder?
V = π(R² − r²)h, where R is the outer radius and r is the inner radius. Square each radius before you subtract.
Is the formula on the SAT sheet?
Yes. The reference sheet in College Board’s digital SAT practice tests gives V = πr²h, with the area of a circle.
Keep exploring
Radius or diameter: does your child mix them up?
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