Volume of a cylinder, explained with examples

By The STEM-Tutor team · Updated October 2026

A cylinder is a prism with a circular cross-section, so its volume is the area of the circle times the height: V = πr²h. It is one of the most common shapes in GCSE problems, from tins and pipes to water tanks.

The formula

Volume = πr²h

r is the radius of the circular end and h is the height (or length) of the cylinder. Think of it as building the cylinder out of thin circular layers: each layer has area πr², and stacking them to height h gives πr² × h. This works for any prism: volume = area of cross-section × length. For GCSE Maths exams in 2025, 2026 and 2027, a formulae sheet is provided with the papers, covering formulae students previously had to memorise; check the sheet for your exam year, but learn the formula anyway, because recalling it quickly saves time.

Volume is measured in cubic units: cm³, m³ and so on.

Worked examples

Example 1: the basic formula

Find the volume of a cylinder with radius 4 cm and height 10 cm, to 1 decimal place.

• V = π × 4² × 10 = 160π.
• V ≈ 502.7 cm³.

Example 2: from the diameter

A tin has diameter 7.4 cm and height 11 cm. Find its volume, to the nearest cm³.

• Radius = 3.7 cm. V = π × 3.7² × 11 = π × 13.69 × 11.
• V ≈ 473 cm³. Always halve the diameter first.

Example 3: in terms of π

Find the volume of a cylinder of radius 3 cm and height 8 cm, leaving your answer in terms of π.

• V = π × 9 × 8 = 72π cm³.

Example 4: finding the height

A cylinder has volume 1000 cm³ and radius 5 cm. Find its height.

• 1000 = π × 25 × h, so h = 1000/(25π).
• h ≈ 12.7 cm.

Example 5: finding the radius

A cylindrical tank 2 m tall holds 6 m³ of water when full. Find its radius.

• 6 = πr² × 2, so r² = 3/π ≈ 0.955.
• r ≈ 0.98 m. Remember to take the square root at the end.

Capacity: volume in litres

Capacity is how much a container holds. The key conversions are:

• 1 litre = 1000 cm³ (and 1 cm³ = 1 ml)
• 1 m³ = 1000 litres

Example 6: litres

A cylindrical water butt has radius 30 cm and height 90 cm. How many litres does it hold?

• V = π × 30² × 90 = 81,000π ≈ 254,469 cm³.
• Divide by 1000: about 254 litres.

Example 7: filling time

Water flows into the butt at 8 litres per minute. How long does it take to fill?

• 254.5 ÷ 8 ≈ 31.8, so about 32 minutes.

Surface area of a cylinder

A closed cylinder has two circular ends and a curved side. If you unroll the curved side, it becomes a rectangle whose width is the circumference 2πr and whose height is h.

Total surface area = 2πr² + 2πrh

For an open cylinder, such as a cup with no lid, use only one circle: πr² + 2πrh. For a tube open at both ends, use only the curved surface, 2πrh.

Example 8: surface area

Find the total surface area of a closed cylinder of radius 4 cm and height 10 cm, to 1 decimal place.

• Ends: 2 × π × 16 = 32π. Curved surface: 2 × π × 4 × 10 = 80π.
• Total = 112π ≈ 351.9 cm².

Hollow cylinders and pipes

For a pipe, find the volume of the outer cylinder and subtract the inner one: V = π(R² − r²)h, where R is the outer radius and r is the inner radius.

Example 9: a pipe

A metal pipe is 2 m long, with outer radius 5 cm and inner radius 4 cm. Find the volume of metal.

• Use the same units: length 200 cm.
• V = π(25 − 16) × 200 = 1800π ≈ 5655 cm³.

Similar cylinders (Higher)

Two cylinders are similar if one is an exact enlargement of the other, with the radius and height both multiplied by the same scale factor k. Then their surface areas are in the ratio k² and their volumes are in the ratio k³. Doubling every length makes the area four times larger and the volume eight times larger, which surprises many students the first time they see it.

Example 10: similar tins

Two similar tins have heights 8 cm and 12 cm. The smaller tin holds 400 cm³. How much does the larger tin hold?

• Length scale factor k = 12/8 = 1.5.
• Volume scale factor = 1.5³ = 3.375, so the larger tin holds 400 × 3.375 = 1350 cm³.

Exam tips

Write the formula before substituting, so the examiner can award method marks. Check the units of every length before you start, and convert to match. Keep π in the calculator, or in the answer if asked, until the final step. Finally, check whether the question wants a volume, a capacity in litres, or a surface area; they need different formulas and units.

Cones and spheres

A cone with the same base and height as a cylinder has exactly one third of its volume: V = ⅓πr²h. A sphere of radius r has volume &frac43;πr³. A classic Higher question shows a sphere fitting exactly inside a cylinder (so the cylinder's height is 2r) and asks you to compare volumes: the sphere is two thirds of the cylinder. Cone and sphere formulas are normally given in the question when needed.

Common mistakes

• Using the diameter instead of the radius.
• Mixing units, such as a radius in cm with a height in m.
• Forgetting that 1 litre is 1000 cm³, not 100.
• Including both circular ends in the surface area of an open container.
• Squaring πr instead of just r.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is the volume of a cylinder on the Foundation paper?

Yes. Volume of a cylinder is on both tiers. Higher papers add harder problems, such as hollow cylinders, rearranging, and comparisons with cones and spheres.

Is the formula given in the exam?

For GCSE exams in 2025, 2026 and 2027, a formulae sheet is provided with the Maths papers, covering formulae students previously had to memorise. Check the sheet for your exam year. Learn the formula anyway: recalling it instantly saves time and avoids copying errors. Cone and sphere formulas are normally provided in the question.

Key takeaways

• V = πr²h: area of the circle times the height.
• Halve the diameter to get the radius.
• 1 litre = 1000 cm³; 1 m³ = 1000 litres.
• Surface area = 2πr² + 2πrh for a closed cylinder.
• For pipes, subtract the inner cylinder from the outer one.

Related guides

• Area of a circle
• Density
• GCSE Maths topics