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.
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
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.
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.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
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
