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title: Surface Area of a Cone
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## Surface Area of a Cone
A cone is a three-dimensional solid that has a circular base, which is connected by a curved surface to its vertex. The curved surface of the cone is formed by a set of line segments that connect the vertex to the circumference of the circle at the bottom.
The `radius of the cone 'r'` is defined by the radius of the circle formed at the bottom. The `slant height 'l'` is the distance from any point on the circle to the vertex of the cone. Lastly, `the altitude 'h'` is defined by the distance measured from the vertex to the cirle's center.
* The `slant height 'h'` is calculated as:
* The `lateral surface area` is given by:
* The `base surface area` is given by:
Hence, the total surface area of the cone is the sum of the `lateral surface area` and the `base surface area`.
#### More Information:
* The derivation for the formula can be found at - [mathopenref.com](https://www.mathopenref.com/coneareaderivation.html)
* The link to a video explaining the derivation is given below: