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 `lateral surface area` is given by: <ahref="http://www.codecogs.com/eqnedit.php?latex=L&space;=&space;\pi&space;r&space;l&space;=&space;\pi&space;r&space;\sqrt{r^2+h^2}"target="_blank"><imgsrc="http://latex.codecogs.com/gif.latex?L&space;=&space;\pi&space;r&space;l&space;=&space;\pi&space;r&space;\sqrt{r^2+h^2}"title="L = \pi r l = \pi r \sqrt{r^2+h^2}"/></a>
* The `base surface area` is given by: <ahref="http://www.codecogs.com/eqnedit.php?latex=B&space;=&space;\pi&space;r^2"target="_blank"><imgsrc="http://latex.codecogs.com/gif.latex?B&space;=&space;\pi&space;r^2"title="B = \pi r^2"/></a>
Hence, the total surface area of the cone is the sum of the `lateral surface area` and the `base surface area`.
<ahref="http://www.codecogs.com/eqnedit.php?latex=A=&space;L&space;+&space;B&space;=&space;\pi&space;r&space;l&space;+&space;\pi&space;r^2&space;=&space;\pi&space;r&space;(l&space;+&space;\pi&space;r)&space;=&space;\pi&space;r&space;(\sqrt{r^2+h^2}+&space;\pi&space;r)"target="_blank"><imgsrc="http://latex.codecogs.com/gif.latex?A=&space;L&space;+&space;B&space;=&space;\pi&space;r&space;l&space;+&space;\pi&space;r^2&space;=&space;\pi&space;r&space;(l&space;+&space;\pi&space;r)&space;=&space;\pi&space;r&space;(\sqrt{r^2+h^2}+&space;\pi&space;r)"title="A= L + B = \pi r l + \pi r^2 = \pi r (l + \pi r) = \pi r (\sqrt{r^2+h^2}+ \pi r)"/></a>