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Surface Area of a Cone

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: $l = \sqrt{r^2+a^2}$
The lateral surface area is given by: $L = \pi r l = \pi r \sqrt{r^2+h^2}$
The base surface area is given by: $B = \pi r^2$

Hence, the total surface area of the cone is the sum of the lateral surface area and the base surface area.

$A= L + B = \pi r l + \pi r^2 = \pi r (l + \pi r) = \pi r (\sqrt{r^2+h^2}+ \pi r)$

More Information:

The derivation for the formula can be found at - mathopenref.com
The link to a video explaining the derivation is given below:

2.8 KiB Raw Blame History

Surface Area of a Cone

More Information:

2.8 KiB

Raw Blame History