cylinder (derived from the Greek language, from the word "roller", "roll") - a geometric body which is limited to the outside surface of the cylindrical called, and the two planes.These planes intersect the surface shape and are parallel to each other.
cylindrical surface - a surface that is obtained translational straight line in space.These movements are such that the selected point of the straight line makes movement along the curve of the flat type.This straight line is called a generator, but a curve - the guide.
cylinder consists of a pair of bases and the side of the cylindrical surface.The cylinders come in several forms:
1. Circular, straight cylinder.Such a cylinder base and a direction perpendicular to the generating line and the symmetry axis exists.
2. The inclined cylinder.He had the angle between the generator and the base line is not straight.
3. Cylinder some form.Hyperbolic, elliptic, parabolic, and others.
area of the cylinder, and the total surface area of any cylinder is found by adding the base area of the figure and the lateral surface area.
formula, which is calculated on the total area of a circular cylinder, right cylinder:
Sp = 2n 2n Rh + R2 = 2n R (h + R).
lateral surface area searched a little more complicated than that of the cylinder as a whole, it is calculated by multiplying the length of the lines forming the perimeter of the cross-section formed by a plane that is perpendicular to the generating line.
given surface area of a circular cylinder, right cylinder recognized by the unfolding of the object.
Scan - a rectangle that has a height h and a length P, which equals around the base.
It follows that the lateral area of the cylinder is equal to the area scan and can be calculated by this formula:
Sb = Ph.
If you take a circular, straight cylinder, for him:
P = 2n R, and the Sb = 2n Rh.
If the tilt cylinder, the lateral surface area should be equal to the product of the length of its generator lines and the perimeter of the cross section which is perpendicular to this generating line.
Unfortunately, there is no simple formula to express the lateral surface area of the inclined cylinder through its height and the parameters of its base.
To calculate the cross-sectional area of the cylinder, it is necessary to know a few facts.If the cross section of its plane intersects the base, there is always the cross section is a rectangle.But these rectangles will vary depending on the position of the cross section.One side axial sectional shape, which is perpendicular to the bases, is the height, and the other - the diameter of the cylinder.And the area of the cross section, respectively, equals the product of one side of the rectangle to the other, perpendicular to the first, or the product of the height of the figure to the diameter of its base.
If the cross section is perpendicular to the base figure, but will not pass through the axis of rotation, the area of this section will be equal to the product of the height of the cylinder and a certain chord.To obtain a chord, you need to draw a circle at the base of the cylinder, the radius of conduct and put on it the distance at which the section.And from this point should be a perpendicular to the radius from the intersection of the circle.The points of intersection are connected to the city center.And the base of the triangle - is the desired chord length of which is sought by the Pythagorean theorem.The Pythagorean theorem is: "The sum of the squares of the two legs is equal to the hypotenuse squared»:
C2 = A2 + B2.
If a section does not affect the base of the cylinder, and the cylinder is circular and straight, the area of this section is the area of a circle.
area of a circle is:
S env.2n = R2.
To find the circle radius R, its length should be divided into 2n C:
R = C \ 2n, where n - the number pi, the mathematical constant, calculated for data circle and equal to 3.14.
