Cylinders
Objective. Calculate cylinder volume and surface area.
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- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A cylinder's volume is found by multiplying the area of its circular cross-section by its height, giving the formula V = πr²h. Its total surface area is the sum of the two circular ends and the curved surface, giving the formula S = 2πr² + 2πrh, where 2πrh comes from unrolling the curved side into a rectangle. For example, a cylinder with radius 3 cm and height 10 cm has volume π × 3² × 10 = 90π cm³ and surface area 2π(3²) + 2π(3)(10) = 18π + 60π = 78π cm². Keeping the radius and height clearly identified from the diagram prevents substitution errors in either formula.
Worked example
A cylinder has radius 4 cm and height 6 cm. Find its volume in terms of π.
- 1The formula for volume is V = πr²h.
- 2Substitute the known values: V = π × 4² × 6.
- 3Calculate 4² = 16, so V = π × 16 × 6.
- 416 × 6 = 96, giving V = 96π.
Answer: 96π cm³
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Practice
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Start practisingCommon mistake. Pupils often forget to double both the circular area term and the curved surface term in the surface area formula, omitting one of the two circular ends. Remember a cylinder has two circular ends, so both 2πr² and 2πrh must appear.
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