determine the area of two identical bases cylinder .There are two related formulas, one of which expresses the parameter of the radius, and the other - of the diameter (D).Since almost easier to measure the diameter, then engage the formula with his participation - Lift this value in the square and get one-fourth of the product of the result by the number Pi: ¼ * π * D².Since this number is irrational, that is, having an infinite number of digits after the decimal point, you should round it, on the basis of the required precision.It is usually only three characters (3,142), and a
more accurate value can be specified, for example, on this page - http://math.com/tables/constants/pi.htm.
expressed in terms of the diameter of the base of the cylinder area of the lateral surface of the figure.Its scan will be a rectangle, one side of which is equal to the perimeter of the base, and the other - the height of the cylinder (h).The circumference of the base is equal to the diameter of the number Pi to calculate the area and multiply by the height: π * D * h.
Summarize the expressions obtained for the base and side surface to obtain a formula of finding surface area cylinder : S = ¼ * π * D² + ¼ * π * D² + π * D * h = ½ *π * D² + π * D * h = π * D * (½ * D + h).For example, if the height of the figure is 35cm, and the diameter of the base is 15cm, the total area its surface with an accuracy of two decimal places is approximately equal to 3.142 * 15 * (1/2 * 15 + 35) = 3.142 * 15 *42,5 ≈ 2003,03sm².
If the base of the cylinder is not a circle, but an ellipse, the base area can be calculated by finding the product of its greater and lesser ® ® axle to pi: R * r * π.To determine the approximate (without the use of integrals) the length of the perimeter of the base, add to the resulting value of the squared difference between the lengths of the major and minor semi-axes, divide the result by the sum of the lengths and increase fourfold: 4 * (R * r * π + (Rr) ²) / (R + r).So you get one side of the rectangle sweep side of the elliptical cylinder , and multiplying it by the height figure (h), get area lateral surface: 4 * (R * r * π + (Rr) ²) / (R +r) * h.Keep expressions base area and a side surface in a formula: S = R * r * π + R * r * π + 4 * (R * r * π + (Rr) ²) / (R + r) * h = 2 *R * r * π + 4 * (R * r * π + (Rr) ²) / (R + r) * h.
- area of the cylinder count