For any figures there is such a term as the height.The height of the measured quantity is usually called a figure-or vertically.At the height of the cylinder is a line perpendicular to its two parallel bases.He also has a generator.The cylinder is the line, which is obtained by rotating the cylinder.It, unlike forming other shapes such as a cone, with the same height.

Consider the formula, which can be used to find the height:

V = πR ^ 2 * H, where R - radius of the cylinder, H - the desired height.

If instead of radius given diameter, the formula is modified as follows:

V = πR ^ 2 * H = 1 / 4πD ^ 2 * H

Accordingly, the height of the cylinder is equal to:

H = V / πR ^ 2 = 4V/ D ^ 2
Also, the height can be determined based on the diameter and area of ​​the cylinder.There is a s
ide area and the total surface area of ​​the cylinder.Part of the surface of the cylinder bounded by a cylindrical surface called a cylinder surface.The total surface area of ​​the cylinder, and includes the area of ​​its grounds.

cylinder surface area is calculated by the following formula:

S = 2πRH

Transforming the expression, get height:

H = S / 2πR

Given a total surface area of ​​the cylinder, calculate the height in a different way.The total surface area of ​​the cylinder is equal to:

S = 2πR (H + R)

First convert this formula as shown below:

S = 2πRH + 2πR

Then find height:

H = S-2πR / 2πR
through the cylinder can be made rectangular.The width of this section will be the same as the diameter of the base, and the length - to form figures that are equal height.If you draw a diagonal cross section through this, we can easily see that the right-angled triangle is formed.In this case the diagonal is the hypotenuse of a triangle, the diameter of a leg, and the second katet- height and the cylinder.Then, the height can be found on the Pythagorean theorem:

b ^ 2 = sqrt (c ^ 2 2 -a ^)