Circle - one of the main curves studied in elementary and higher mathematics. The circle, in turn, represents the figure which is in the section of many bodies of rotation. The cylinder and a cone concern those, in particular.
Instruction
1. A circle is called the locus, equidistanted from the center. It is the closed curve at which all points are constant. The circle forms the circle basis. Cut sausage long loaf - and circles, equal on length, will turn out. Respectively, the film which is a long loaf fringing will be cut on a circle. The circle is also sphere section. For receiving the biggest of them cut a sphere in the middle. It passes through the center of a sphere and has the maximum length of a circle.
2. Draw a sphere with some diameter equal to D. Carry out section strictly on its center therefore the circle with a diameter equal to diameter of a sphere will turn out. Rotating this circle round its pivot-center, receive a sphere of the same diameter, as initial. If to rotate not a circle, but a circle, instead of a sphere the hollow figure called the sphere will turn out. To calculate circle length in this example, it is necessary to calculate circle length. In number this parameter is equal to circle length. Calculate it, using the formula given below: C=πD=2πR.Такой a way of the solution of a task is applied only when the radius or diameter of a circle are known. However in practice the tasks about circles requiring the multi-stage solution occur in textbooks on geometry.
3. Draw a cone at which section is carried out through the middle of height parallel to the basis. Its height is equal h, and length of forming is l. From the drawing received by you it is visible that to find the radius of the circle formed as a result of cone section by the plane it is necessary to apply standard Pythagorean theorem. As section is carried out in the middle of a cone, length of height is equal h/2, and length of forming will be l/2. Respectively, on Pythagorean theorem find radius on the formula shown below: R= √ (l/2) ^2-(h/2) ^2. From this it follows that length of this circle can be calculated as follows: With =2πR=2π √ (l/2) ^2-(h/2) ^2.