The surface area of a cone
I can calculate the surface area of a cone.
The surface area of a cone
I can calculate the surface area of a cone.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- The slanted surface of a cone can be cut into congruent triangles.
- These form a parallelogram with dimensions of the slanted length and half of the circumference of the base.
- The area of the slanted surface can be written as πrl
- The surface area of the cone is therefore πrl + πr^2
- The slanted length can be calculated from the height of the cone and radius of the base
Keywords
Cone - A circular cone is a 3D shape that has a circular base and one curved surface that narrows from the base to a fixed point called the apex/vertex.
Right cone - A line drawn through the apex and centre of the base of a right circular cone will be perpendicular to the base.
Apex - The apex is the point (vertex) which is the greatest perpendicular distance from the base.
Common misconception
When finding the surface area of the cone, pupils may find the curved surface area but forget to include circular base of the cone.
By re-reading the question, and inspecting any given diagram, pupils can check if the cone is open or closed and therefore if they need to include the circular base in their calculation.
To help you plan your year 11 maths lesson on: The surface area of a cone, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: The surface area of a cone, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the 2D and 3D shape: surface area and volume (pyramids, spheres and cones) unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
Surface area of a sphere -
$$4 \pi r^2$$
Volume of a sphere -
$$\frac{4}{3} \pi r^3$$
Surface area of a cylinder -
$$2 \pi rh + 2 \pi r^2$$
Volume of a cylinder -
$$ \pi r^2 h$$
Exit quiz
6 Questions
The radius of the sector is… -
10 cm
The arc length of the sector is… -
8𝜋 cm
The area of the sector is… -
40𝜋 cm²
