1. Preliminary understanding of cone area
A cone is a geometric figure surrounded by a circle and a triangle whose vertices are not in the same plane.
The bottom of the cone is round, the distance from the apex to the center of the circle is called height, and the hypotenuse is called oblique height.
If the cone is unfolded, a sector and a triangle can be obtained, and the sum of their areas is the surface area of the cone.
An object surrounded by a straight line formed by one right-angled side of a right-angled triangle as the rotation axis and the other two sides rotating is called a cone; A cone consists of a vertex, a side surface and a bottom surface, and the distance from the vertex to the center of the bottom surface is the height of the cone; A cone has two faces, the bottom is round and the side is curved; Let the cone expand along the generatrix, which is a sector.
2. Calculate the cone bottom area
In the surface area formula of a cone, πr? Is the cone bottom area.
If the bottom radius r is known, it can be calculated by πr? Calculate the cone bottom area.
3. Calculate the lateral area of the cone.
In the formula, the lateral area of the cone is expressed as πrl, in which the oblique height L needs to be obtained by Pythagorean theorem.
Pythagorean theorem refers to the principle that the square of hypotenuse in right-angled triangle is equal to the sum of squares of right-angled sides, that is, L? =h？ +r？ .
Knowing the radius and height of the cone bottom, we can calculate the oblique height, and then find out the lateral area of the cone.
4. Comprehensive calculation of cone surface area
The surface area of a cone is equal to the sum of the bottom area and the side area, that is, S=πrl+πr? .
Therefore, if the radius and height of the cone bottom are known, the surface area of the whole cone can be calculated by formula.
In a word, to calculate the surface area of a cone, we need to master the concepts of bottom radius, height and length of hypotenuse, and be familiar with the application of Pythagorean theorem. In the initial learning stage, the bottom area and lateral area can be calculated first, and then the whole surface area can be calculated together. In the study of advanced mathematics, you will also learn more complicated calculation methods of cone volume.