Cylinder volume questions appear regularly on both Foundation and Higher GCSE papers. A cylinder is simply a circular prism, so the formula follows the same logic — area of the circular cross-section multiplied by the height. This guide walks through the formula, reverse problems, and real-world applications.
What Is the Volume of a Cylinder?
A cylinder is a 3D shape with two identical circular faces connected by a curved surface. Its volume is the amount of space it encloses.
Because a cylinder is a prism with a circular cross-section, the volume formula is the area of the circle (pi r²) multiplied by the height (h). This formula is not given on the exam formula sheet, so you must memorise it.
Cylinders appear in many real-world contexts — water tanks, cans, pipes, and candles. Exam questions often present the cylinder in a practical scenario and ask you to calculate capacity or find a missing dimension.
Key Formulas
Step-by-Step Method
- Check whether you have been given the radius or the diameter. If given the diameter, halve it.
- Substitute into V = pi r² h.
- Calculate, rounding as instructed or leaving in terms of pi.
Worked Example 1 — Foundation Level
Question: A cylinder has radius 4 cm and height 10 cm. Find its volume to 1 decimal place.
Working: V = pi r² h V = pi × 4² × 10 V = pi × 16 × 10 V = 160pi V = 502.654...
Answer: 502.7 cm³ (1 d.p.)
Worked Example 2 — Higher Level
Question: A cylindrical water tank has a volume of 5000 cm³ and a radius of 8 cm. Find its height to 1 decimal place.
Working: V = pi r² h 5000 = pi × 8² × h 5000 = 64pi × h h = 5000 ÷ (64pi) h = 5000 ÷ 201.061... h = 24.867...
Answer: 24.9 cm (1 d.p.)
Worked Example 3 — Exam Style
Question: A cylindrical can has diameter 7.4 cm and height 11 cm. Find the volume of the can in cm³. Give your answer to 3 significant figures.
Working: Radius = 7.4 ÷ 2 = 3.7 cm V = pi × 3.7² × 11 V = pi × 13.69 × 11 V = 150.59pi V = 473.057...
Answer: 473 cm³ (3 s.f.)
Common Mistakes
- Using the diameter instead of the radius. The formula requires r, not d. If the question gives the diameter, divide by 2 first.
- Forgetting to square the radius. Writing pi × r × h gives the wrong answer. You must square the radius before multiplying by the height.
- Confusing volume and surface area formulas. Volume uses pi r² h (cubic units); curved surface area uses 2pi rh (square units). Check your units to confirm you have used the right formula.
Exam Tips
- This formula is not on the exam formula sheet — learn V = pi r² h by heart.
- For reverse problems (finding r or h), rearrange the formula before substituting. Show the rearrangement step for a method mark.
- In real-world context questions, check whether the answer needs converting (e.g. cm³ to litres: 1000 cm³ = 1 litre).
Practice Questions
Q1 (Foundation): A cylinder has radius 5 cm and height 9 cm. Find its volume to the nearest whole number.
Q2 (Foundation): A cylindrical tin has diameter 8 cm and height 12 cm. Find its volume to 1 decimal place.
Q3 (Higher): A cylinder has a volume of 800 cm³ and a height of 10 cm. Find its radius to 2 decimal places.
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Related Topics
Summary
- A cylinder is a circular prism with volume V = pi r² h.
- Always use the radius (not the diameter) in the formula.
- To find a missing dimension, rearrange the formula before substituting.
- This formula is not provided on the exam formula sheet — memorise it.
- In real-world problems, remember that 1000 cm³ = 1 litre for capacity conversions.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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