The net of the cone. Deduce the area formula.

The cone surface spread on a plane is formed by a circle  and  by a circular section.

Draw the cone net in your notebook.

Write down the base area formula in your notebook.

Deduce the formula for the curved surface area.

The curved surface area is equivalent to a circular section.
To deduce its formula we use the triangle area formula, because we can consider it as a curved triangle.

Remember that the triangle area formula is (1/2) . base . perpendicular height

s = (1/2) · b · h
The arch of this circular sector is the base of this triangle, and it is the circumference of the cone base.

l = 2 · π · r

The height of this curved triangle is the slant height of the cone.

To find the total surface area of a cone, add up the base surface area and the curved surface area.