Circle call circle border - the closed curve which length depends on the circle size. This closed line divides the plane, infinite by definition, into two unequal parts, one of which continues to remain infinite, and another can be measured and is called the area of a circle. Both sizes - length of a circle and the area of a circle - are defined by its sizes and can be expressed one through another or through diameter of this figure.
Instruction
1. For calculation lengthscirclesof (L) with use of the known length of diameter (D) not to do without Pi's number - a mathematical constant which, actually, and expresses interdependence of these two parameters of a circle. Multiply Pi's number and diameter to receive required size L = π*D. Often instead of diameter in initial conditions the radius (R) of a circle is given. In this case replace in a formula diameter with the doubled radius: L = π*2*R. For example, at radius in 38 cm length of a circle has to be about 3.14*2*38 = 238.64 cm.
2. It is impossible to calculate the area of a circle (S) with the known diameter (D) without use of number of Pi too - multiply it by the squared diameter, and you divide result into the four: S = π*D²/4. With use of radius (R) this formula on one mathematical operation will become shorter: S = π*R². For example, if radius is equal to 72 cm, the area has to be 3.14*722 = 16277.76 cm².
3. If it is necessary to express length of a circle (L) through the area of a circle (S), make it with use of the formulas given in two previous steps. In them there is one general parameter of a circle - diameter, or the doubled radius. At first express unknown radius through the known area of a circle to receive such expression: √(S/π). Then substitute this value in a formula from the first step. The final formula of calculation of length of a circle for the known area of a circle has to look so: L = 2 * √ (π*S). For example, if the circle occupies the space in 200 cm², length of its circle will be equal 2 * √ (3.14*200) = 2 * √ 628 ≈ 50.12 cm.
4. The return task - finding of the area of a circle (S) on the known length of a circle (L) - will demand from you the similar sequence of actions. At first express from a formula of the first step radius through circle length - at you such expression has to turn out: L/(2*π). Then set up him in a formula of the second step - the result has to look so: S = π * (L / (2*π)² = L² / (4*π). For example, the area of a circle with a length of circle of 150 cm has to be about 1502 / (4*3.14) = 22500/12.56 ≈ 1791.40 cm².