Surface Area of a Cylinder – Differentiated Worksheet with Worked Solutions (KS3 and GCSE)

This worksheet takes students from finding surface area using a net through to working backwards from a given surface area and solving multi-step real-life problems. It suits KS3 and GCSE Foundation and Higher students. The worked solutions come as a separate document, which makes the pack useful for classwork, homework, intervention and revision.

The worksheet has five colour-coded levels, so students can start where they need to and move up as their confidence grows. Each level is on its own page with a matching coloured border, which makes it easy to print only the levels a class or student needs. Every question has a square grid for working out and a clear answer line, and the cylinders are coloured to help students tell the circular faces from the curved surface.

Green (Practice): four cylinder nets with no scaffolding. Students find the area of the two circles and the rectangle, and two of the nets give the diameter rather than the radius.
Amber (Further practice): four cylinders with whole-number measurements, some giving the radius and some the diameter. The cylinders are drawn upright, lying down and tilted, so students learn to spot the radius and height whatever the orientation.
Red (Further developing understanding): four cylinders in different positions with decimal radii and diameters, some in centimetres and some in metres. This builds accuracy and careful rounding.
TIF (Problem solving): six questions where students work backwards to find a missing height, length or radius. They cover:
working from a total surface area given as a decimal or in terms of π
working from a curved surface area
an algebraic question where the height is a multiple of the radius
two illustrated real-life problems: painting the inside of an open farm water tank, where only one circle is used, and an advert wrapped around a shopping-mall pillar, which uses the curved surface only
TIEF (Real-life challenge): one extended, illustrated problem about painting a water tank on a villa roof in Dubai. Students choose which surfaces to include, account for two coats, convert area into litres of paint, and compare tin sizes and prices to find the cheapest way to buy the paint.

The worked solutions set out every step for all 19 questions. They show exact answers in terms of π alongside decimal answers, keep full calculator values until the final step, and highlight common pitfalls such as forgetting to halve the diameter, including both circles on an open tank, or rounding down the number of paint tins.

Skills covered: surface area of cylinders, circumference and area of circles, nets of 3D shapes, working with π, rearranging to find unknown lengths, unit conversion, rounding, and problem solving in context.