Sheet № 103 · Foundation + Higher · AQA · Edexcel · OCR
Volume of a Cylinder –
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.
§Key definitions
Question:
A cylinder has radius 4 cm and height 10 cm. Find its volume to 1 decimal place.
Answer:
502.7 cm³ (1 d.p.)
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.
§Formulas to memorise
V = pi r² h, where r is the radius and h is the height
To find h from volume: h = V ÷ (pi r²)
Substitute into V = pi r² h.
V = pi r² h
V = pi × 4² × 10
V = pi × 16 × 10
V = 160pi
V = 502.654...
h = 5000 ÷ (64pi)
h = 5000 ÷ 201.061...
Worked example
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...
⚠ 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).