Explain which body is called a cone. Derive the formula for the total surface area of a cone.

A cone is a body whose base consists of a circle whose points do not lie on the plane of this circle, as well as segments that connect the top and all points of the base.

To derive the total area of ​​a cone, we need previous knowledge of calculating areas: lateral area and area of ​​a circle.

The lateral surface area: Sbok = π * R * L, where π is the number of pi, R is the radius, L is the circumference. Or Sbok = π * R * sqrt (R ^ 2 * H ^ 2), where H is the height.

Area of ​​a circle: Sosn = π * R ^ 2

Then we can express the area of ​​the full surface of the cone, which will be the sum of these two areas: S = π * R * L + π * R ^ 2 or S = π * R * sqrt (R ^ 2 * H ^ 2) + π * R ^ 2 = π * R * sqrt ((R ^ 2 * H ^ 2) + R)