GCSE MATHS • HIGHER TIER

Cylinders Made Simple

Understand cylinder properties and calculate volume, surface area and missing dimensions accurately.

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Worked proofs

Cylinders in Four Moves

1

Identify

Find the radius and height, converting diameter to radius when needed.

2

Choose

Decide whether the question asks for volume, surface area or a missing dimension.

3

Substitute

Put the values carefully into the correct cylinder formula.

4

Calculate

Use π accurately, round appropriately and include the correct units.

What You’ll Learn

Recognise the properties of a cylinder.

Understand radius, diameter and height.

Calculate the volume of a cylinder.

Calculate total surface area.

Find a missing radius from volume.

Use π accurately and round answers appropriately.

Use correct square and cubic units.

Key Rules

Radius and Diameter

The radius is half the diameter. Radius = Diameter ÷ 2.

Volume Formula

Volume = πr²h

Surface Area Formula

Surface Area = 2πr² + 2πrh

Square the Radius

Always use r², not just r, in the formulas.

Correct Units

Use cm², m² for surface area and cm³, m³ for volume.

Worked Proof: Cylinder

Step-by-Step Method

  • Identify the Radius and Height
  • Decide What You Need to Find
  • Choose the Correct Formula
  • Substitute the Values
  • Calculate Carefully
  • Add the Correct Units
  • Round at the End

More Worked Examples

1

Question: Radius = 4 cm, Height = 10 cm.

Surface Area = 2π(4²) + 2π(4)(10)

= 32π + 80π
= 112π
≈ 351.9 cm²
Answer: 351.9 cm².

2

Question: Radius = 6 cm, Height = 9 cm.

Surface Area = 72π + 108π

= 180π
≈ 565.5 cm²
Answer: 565.5 cm².

3

Question: Volume = 314 cm³, Height = 10 cm. Find the radius.

314 = πr²(10)

r² ≈ 10
r ≈ 3.16 cm
Answer: 3.16 cm.

4

Question: Radius = 7 cm, Height = 12 cm.

Volume = π × 49 × 12

= 588π
≈ 1847.3 cm³
Answer: 1847.3 cm³.
  • Common GCSE Mistakes
  • Using the diameter instead of the radius.
  • Confusing volume and surface area formulas.
  • Forgetting to square the radius.
  • Omitting cubic or square units.
  • Rounding too early.
  • Exam Tips
  • Check whether the given measurement is radius or diameter.
  • Write the correct formula before substituting values.
  • Square the radius carefully.
  • Keep π on the calculator until the final step.
  • Round only at the end unless told otherwise.
  • Use cm² for surface area and cm³ for volume.

Skills Used in Cylinder

Cylinder Properties

Radius and Diameter

Volume

Surface Area

Mensuration

π Calculations

Missing Dimensions

Square & Cubic Units

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Printable Worksheet

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Exam-Style Questions

Timed questions to build confidence for the real exam.

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Watch the Cylinder Tutorial

Step-by-step walkthroughs of Cylinder with clear methods and exam tips.

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Frequently Asked Questions

A cylinder is a 3D shape with two identical circular faces connected by a curved surface.

Volume = πr²h.

Surface Area = 2πr² + 2πrh.

Divide the diameter by 2 to find the radius before using the formula.

Use cubic units such as cm³.

Keeping full calculator values until the end helps maintain accuracy.