G17h – Surface area of cylinders, spheres, and cones

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Prerequisites

Formulas

\( \text{Surface area of sphere }=4 \pi r^{2} \text{, where }r \text{ is the radius }\)\(\text{of the sphere.}\)
  • AQA, Edexcel, and OCR will provide this formula in the exam in any relevant questions.
  \(\text{Curved surface area of a cone }= \pi rl \text{, where }r \text{ is the}\) \(\text{radius and }l \text{ is the slant height of the cone.}\)
  • AQA, Edexcel, and OCR will provide this formula in the exam in any relevant questions.
  \( \text{Curved surface area of cylinder }=2 \pi rh \text{, where }r \text{ is}\)\(\text{ the radius and }h \text{ is the height of the cylinder.}\)
  • You need to learn this formula – or at least understand where it comes from.
 

Surface area of cylinders, spheres, and cones

Teacher resources

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  • Slides in PPTX (with click-to-reveal answers)
  • Slides in PDF (one slide per page, suitable for importing into IWB software)
Links to past exam questions

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Interactive GeoGebra activity

Drag the slider to watch an animation of a cylinder being unfolded into its net. This should help illustrate why the surface area of a cylinder consists of the areas of two circles and a rectangle.
With thanks to Tim Brzezinski, whose Unwrapping a cylinder worksheet is available here. Material modified and embedded here under the CC-BY-SA 3.0 license.

Activity: Do you have enough paint?

In the real world

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What next?