The formula for deriving a cylinder's height involves dividing its volume by the area of one of its end faces. If the physical cylinder is present, measuring the shortest distance along the curved side from one end to the other end is the easiest way to find its height.
- Determine whether to calculate or measure the height of the cylinder
If you have access to the actual cylinder, take a point along the edge of one face of the cylinder and another point along the edge of the cylinder's other face such that a straight line along the curved side connects the two points on the edge and the line is perpendicular to both faces of the cylinder. The length of this line is its height. In the context of a math problem, you should calculate it based on other parameters given in the problem. If you know the volume of the cylinder, and either an end face's area or parameters from which the area can be derived, you can calculate the height. This is because the formula for volume of a cylinder is V = Bh, where B is the area of the base and h is the height. In the context of a cylinder with circular faces, the formula can therefore also be expressed as V = ?*r^2 * h, where r is the radius of one of the circular faces.
- Calculate the area of an end face of the cylinder if it is not known
For a cylinder with circular end faces, if the radius "r" is known, calculate the area using the formula A = ?(r^2). If the end faces are elliptical, find the area using the lengths of the semi-major and semi-minor axes using the formula A = ?ab, where a and b are the semi-major and semi-minor axes, respectively.
- Divide the volume by the area of the end face
Divide the cylinder's volume by the area of the end face to derive the height of the cylinder.