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Volume of a Cylinder

FoundationHigherAQAEdexcelOCR

Master volume of a cylinder for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers calculating the volume of a cylinder and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Volume of a cylinder = πr²h.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Higher

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Topic overview

A cylinder is a prism with a circular cross-section, so its volume is the area of the circle multiplied by the height: \(V = \pi r^2 h\).

The formula needs the radius, not the diameter. Because the radius is squared, using the diameter by mistake makes the answer four times too large — the same trap as with circle area.

Height is sometimes called length, depending on whether the cylinder stands upright or lies on its side. Either way, it is the distance between the two circular faces, measured perpendicular to them.

Revision notes

The formula

\(V = \pi r^2 h\). Find the circle's area first, then multiply by the height.

For radius \(4\)cm and height \(10\)cm: \(\pi \times 16 \times 10 = 160\pi\)cm³, or \(502.7\)cm³ to one decimal place.

Radius versus diameter

Halve the diameter before substituting.

A cylinder of diameter \(12\)cm has radius \(6\)cm, giving \(\pi \times 36 \times h\). Using \(12\) would give four times the correct answer.

Working backwards

If the volume is known, substitute and rearrange to find a missing dimension.

With \(V = 100\pi\)cm³ and \(r = 5\)cm: \(100\pi = \pi \times 25 \times h\), so \(h = 4\)cm.

Key points

  • Cylinder volume is \(V = \pi r^2 h\).
  • The formula uses the radius.
  • Halve the diameter if necessary.
  • Square the radius before multiplying.
  • Volume is in cubed units.
  • The height is perpendicular to the circular faces.

Worked examples

Example 1

Find the volume of a cylinder with radius \(3\)cm and height \(8\)cm, in terms of \(\pi\).

Working

\[\pi \times 3^2 = 9\pi\]find the circle's area
\[9\pi \times 8\]multiply by the height
\[= 72\pi\text{cm}^3\]state the volume

Example 2

Find the volume of a cylinder with diameter \(10\)cm and height \(6\)cm, in terms of \(\pi\).

Working

\[r = 5\text{cm}\]halve the diameter
\[\pi \times 25 \times 6\]substitute into the formula
\[= 150\pi\text{cm}^3\]state the volume

Example 3

A cylinder has volume \(144\pi\)cm³ and radius \(6\)cm. Find its height.

Working

\[144\pi = \pi \times 36 \times h\]substitute the known values
\[144 = 36h\]divide both sides by pi
\[h = 4\text{cm}\]solve for the height

Common mistakes

  • Using the diameter as the radius.

    This gives four times the correct volume, because the radius is squared.

  • Using squared units.

    Volume needs cm³, not cm².

  • Multiplying before squaring.

    Square the radius first, then multiply by π and the height.

  • Confusing volume with surface area.

    Volume fills the shape; surface area covers it.

Exam tips

  • Write the radius down before substituting.
  • Square the radius as a separate step.
  • Leave answers in terms of π when exact values are wanted.
  • Always use cubed units.

Key terms

Cylinder
A prism with a circular cross-section.
Radius
The distance from the centre to the edge of the circle.
Height
The distance between the two circular faces.
Cubed units
Units such as cm³ used for volume.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.