The following formula gives you the surface area of a cone.
Here’s a little more background on the lateral area:
The lateral area of a cone is one “triangle” that’s been rolled into a cone shape like a snow-cone cup (it’s only kind of a triangle because when flattened out, it’s actually a sector of a circle with a curved bottom side). Its area is
Now for a cone problem:
Here’s the proof diagram.
For the surface area, the only other thing you need is the slant height, l. The slant height is the hypotenuse of the 30-60-90 triangle, so it’s just twice the radius, which makes it
Now plug everything into the cone surface area formula:
