What is the formula for the volume of a cylinder?

V = πr²h, where r is the radius of the circular end and h is the height. Find the area of the circle (πr²), then multiply by the height. A cylinder with radius 4 cm and height 10 cm has volume 160π ≈ 502.65 cm³.

How do I find the volume of a cylinder from the diameter?

Halve the diameter to get the radius first, then use V = πr²h. A tank with diameter 1.2 m and height 1.5 m has radius 0.6 m, so V = π × 0.36 × 1.5 ≈ 1.70 m³.

How do I change the volume of a cylinder into litres?

1000 cm³ is 1 litre and 1 m³ is 1000 litres. So a volume of 2500 cm³ is 2.5 L, and 1.7 m³ is 1700 L. Work out the volume in cm³ or m³ first, then convert.

How do I find the height of a cylinder from its volume?

Rearrange V = πr²h to h = V ÷ (πr²). Work out πr² first, then divide the volume by it. A 1000 cm³ cylinder with radius 5 cm has height 1000 ÷ (25π) ≈ 12.73 cm.

Is the volume of a cylinder the same as its surface area?

No. Volume is the space inside, measured in cubic units like cm³. Surface area is the total area of the outside (two circles plus the curved side), measured in square units like cm². They use different formulas.

What year level learns the volume of a cylinder?

In the Victorian Curriculum 2.0, Year 8 finds the volume of right prisms, and cylinders are part of Year 9 measurement along with their surface area. Year 10 uses them in composite solids, and Year 10A adds cones and spheres.

How to Find the Volume of a Cylinder: Formula, Examples and Calculator (Years 8 to 10)

The volume of a cylinder formula

V = \pi r^2 h

Every prism has volume $V = A \times h$ : the area of its cross-section times its height. A cylinder's cross-section is a circle, with area $\pi r^2$ , so

V = \underbrace{\pi r^2}_{\text{area of the circle}} \times h

$r$ is the radius of the circular end (centre to edge).
$h$ is the height: the distance between the two circular ends. If the cylinder is lying down, like a pipe or a log, the "height" is its length.
Volume is measured in cubic units: mm³, cm³ or m³.

Volume from the radius and height

Worked example

Find the volume of a cylinder with radius $4$ cm and height $10$ cm.

V = \pi r^2 h

V = \pi \times 4^2 \times 10

V = \pi \times 16 \times 10 = 160\pi

V \approx 502.65 \text{ cm}^3

$160\pi$ cm³ is the exact answer; $502.65$ cm³ is rounded to 2 decimal places. Square the radius before anything else: $4^2 = 16$ , not $8$ .

Volume from the diameter

Worked example

A cylindrical water tank has diameter $1.2$ m and height $1.5$ m. Find its volume.

r = \frac{1.2}{2} = 0.6 \text{ m}

V = \pi \times 0.6^2 \times 1.5

V = \pi \times 0.36 \times 1.5 = 0.54\pi

V \approx 1.70 \text{ m}^3

Questions about tanks, cans and pipes usually give the diameter, because that's what you can measure with a tape. Halve it before you square it. Using the diameter by mistake makes the answer four times too big.

Volume of a cylinder calculator (with working)

Find the volume from the radius or diameter, or work back to the height or radius. You’ll get the exact answer in terms of π where it’s tidy, decimals rounded to 2 decimal places, and litres when the units are mm, cm or m.

Radius (r)Height (h)Units (optional)

V = 160π ≈ 502.65 cm³

Volume of a cylinder: $V = \pi r^2 h$ (area of the circle times the height)
Area of the circular base: $\pi r^2 = \pi \times 4^2 = 16\pi \approx 50.27\text{ cm}^2$
Multiply by the height: $V = 16\pi \times 10 = 160\pi \approx 502.65\text{ cm}^3$
Capacity: $1000 \text{ cm}^3 = 1$ L, so the cylinder holds ≈ 0.50 L
Decimals are rounded to 2 decimal places using the π button. If your teacher says to use 3.14, your answer may be slightly different.

Use the same units for every length. Volume units are cubed (cm³), lengths are not.

Volume of a cylinder in litres (capacity)

Capacity is how much a container holds. Work out the volume, then convert:

Volume	Capacity
$1$ cm³	$1$ mL
$1000$ cm³	$1$ L
$1$ m³	$1000$ L

Worked example

A drink can has diameter $6.6$ cm and height $12$ cm. How many millilitres does it hold, to the nearest millilitre?

r = 3.3 \text{ cm}

V = \pi \times 3.3^2 \times 12

V = \pi \times 10.89 \times 12 = 130.68\pi

V \approx 410.54 \text{ cm}^3

Since $1$ cm³ $= 1$ mL, the can holds about $411$ mL.

For the tank above, $1.70$ m³ is about $1.70 \times 1000 = 1700$ L. (Using the unrounded value, $0.54\pi \times 1000 \approx 1696$ L. Round at the end, not in the middle.)

Finding the height or radius from the volume

Rearrange $V = \pi r^2 h$ for the measurement you need:

h = \frac{V}{\pi r^2} \qquad\qquad r = \sqrt{\frac{V}{\pi h}}

Worked example: missing height

A cylindrical jug holds $1$ L ( $1000$ cm³) and has radius $5$ cm. How tall is it on the inside?

h = \frac{1000}{\pi \times 5^2} = \frac{1000}{25\pi}

h \approx 12.73 \text{ cm}

Worked example: missing radius

A cylinder has volume $500$ cm³ and height $12$ cm. Find its radius.

r^2 = \frac{500}{\pi \times 12} \approx 13.26

r = \sqrt{13.26\ldots} \approx 3.64 \text{ cm}

Check by substituting back: $\pi \times 3.64^2 \times 12 \approx 499.5$ , which is $500$ allowing for rounding.

Half cylinders and hollow cylinders (pipes)

A half cylinder (like a trough or a tunnel) has half the volume: $V = \dfrac{1}{2}\pi r^2 h$ .

A hollow cylinder (a pipe or tube) is a big cylinder with a smaller one removed. Subtract the inside from the outside:

V = \pi R^2 h - \pi r^2 h

V = \pi (R^2 - r^2) h

where $R$ is the outer radius and $r$ is the inner radius.

Worked example: a pipe

A concrete pipe is $20$ cm long, with outer radius $5$ cm and inner radius $4$ cm. Find the volume of concrete.

V = \pi(5^2 - 4^2) \times 20

V = \pi \times 9 \times 20 = 180\pi

V \approx 565.49 \text{ cm}^3

Subtract the squares, not the radii: $5^2 - 4^2 = 9$ , but $(5 - 4)^2 = 1$ .

Common mistakes

Using the diameter as the radius. Halve the diameter first. Otherwise the answer is four times too big.
Squaring the wrong thing. Only the radius is squared. $\pi r^2 h$ means $\pi \times r \times r \times h$ , not $(\pi r)^2 h$ or $\pi r^2 h^2$ .
Mixed units. A radius in cm and a height in m won't work. Convert so every length is in the same unit before you multiply.
Mixing up volume and surface area. Volume is in cubic units (cm³) and uses $\pi r^2 h$ . Surface area is in square units (cm²) and uses $2\pi r^2 + 2\pi r h$ .
Rounding too early. Keep the full value of $\pi r^2$ in your calculator and only round the final answer.

Practice questions with answers

Try each one before you open the answer. Decimal answers use the π button and are rounded to 2 decimal places unless the question says otherwise.

Find the volume of a cylinder with radius $3$ cm and height $7$ cm.
Show the answer
$V = \pi \times 3^2 \times 7 = 63\pi \approx 197.92$ cm³
Find the volume of a cylinder with diameter $10$ m and height $4$ m.
Show the answer
$r = 5$ , so $V = \pi \times 5^2 \times 4 = 100\pi \approx 314.16$ m³
Find the volume of a cylinder with radius $2.5$ cm and height $8$ cm.
Show the answer
$V = \pi \times 2.5^2 \times 8 = 50\pi \approx 157.08$ cm³
A rainwater tank is a cylinder with radius $0.9$ m and height $2$ m. How many litres does it hold?
Show the answer
$V = \pi \times 0.9^2 \times 2 = 1.62\pi \approx 5.089$ m³. Since $1$ m³ $= 1000$ L, it holds about $5089$ L.
A cylinder has volume $750$ cm³ and radius $4$ cm. Find its height.
Show the answer
$h = \dfrac{750}{\pi \times 4^2} = \dfrac{750}{16\pi} \approx 14.92$ cm
A cylinder has volume $2000$ cm³ and height $10$ cm. Find its radius.
Show the answer
$r^2 = \dfrac{2000}{10\pi} \approx 63.66$ , so $r \approx 7.98$ cm
A water trough is half a cylinder, with radius $0.3$ m and length $2$ m. Find its capacity in litres.
Show the answer
$V = \dfrac{1}{2} \times \pi \times 0.3^2 \times 2 = 0.09\pi \approx 0.2827$ m³, which is about $282.7$ L.
A pipe is $50$ cm long, with outer diameter $10$ cm and inner diameter $8$ cm. Find the volume of material in the pipe.
Show the answer
Outer radius $5$ , inner radius $4$ . $V = \pi(5^2 - 4^2) \times 50 = 450\pi \approx 1413.72$ cm³

Volume by year level

Following the Victorian Curriculum 2.0. Schools sequence topics differently, so check your course.

Year 8

Volume

Volume of right prisms as area of the cross-section times the height, and capacity in mL and L.

Worksheets and topic test · Free PDF with answers

Year 9

Surface area and volume

Volume and surface area of cylinders, plus composite solids made from prisms and cylinders.

Worksheets and topic test · Free PDF with answers

Year 10

Surface area and volume

Composite objects, including hollow and drilled solids, and capacity problems like tanks and packaging.

Worksheets and topic test · Free PDF with answers

Year 10A

Surface area and volume of pyramids, cones and spheres

Cones and spheres. A cone has one third of the volume of a cylinder with the same radius and height.

Worksheets and topic test · Free PDF with answers

How to find the volume of a cylinder

The volume of a cylinder formula

Volume from the radius and height

Volume from the diameter

Volume of a cylinder calculator (with working)

Volume of a cylinder in litres (capacity)

Finding the height or radius from the volume

Half cylinders and hollow cylinders (pipes)

Common mistakes

Practice questions with answers

Volume by year level

Volume of a cylinder: common questions

More maths help, Years 7 to 10

Got a volume question wrong in homework?