i will give you a link to a page that explains it. http://mathworld.wolfram.com/CylindricalSegment.html
Given only the lateral area, you cannot determine the diameter.
What do you mean by "exact measurement"? Do you wish to determine the cylinder's height? Its diameter? Its surface area? Its volume?
pi r^2 h is used to determine the volume of a cylinder because when determing the area of a shape you first have to determine the area of the the base of the object and then multiply it by the height. The base of a cylinder is a circle and to find the area of a circle you use pi r^2 and hence the reason why pi r^2 is used to find the volume of the cylinder.
a line segment has no area. By definition a line segment is a part of a line, thus it has no area
The surface area does not provide enough information to determine the dimensions of the cylinder. It could be a tall thin cylinder or a squat one. It is possible for two such to have the same surface area but vastly different volumes.
A cylinder is a tree-dimensional figure with two parallel bases bounded by congruent circles and a curved lateral surface that connects the circles. The height, h, of a cylinder is the length of any perpendicular segment drawn from a point on the base to the plane containing the other base. A cylinder is a right cylinder if the segment joining the centers of the bases is perpendicular to the planes of the bases. Otherwise, the cylinder is oblique. If a right cylinder has a height h and a base with radius r, then the lateral area L.A. is given by the formula: L.A. = 2(pi)(r)(h) The surface area S.A. is given by the formula: S.A. = L.A. + 2(pi)(r^2). Thus, the area of the cylinder's base is (pi)(r^2).
Area of base X height Area of base is pi X r2 r is radius pi = 3.1416
The volume, V, of a cylinder with base of radius r is the product of the area, B, of a base and the height, h, of the cylinder.V = Bh or V = (pi)(r^2)h(A cylinder is a right cylinder if the segment joining the centers of the bases is perpendicular to the planes of the bases. Otherwise the cylinder is oblique.)
Your question is unanswerable, as asked, but you can easily calculate the volume of a cylinder once you know its size. To determine the volume of a cylinder, you need to find the area of the circle, and then multiply that by the height of the cylinder. (Pi X Radius squared X height) Good luck.
The answer will depend on what the formula is for: the perimeter or area of the segment.
A segment is the area within a circle enclosed by an arc and a chord
The surface area of a cylinder can be derived from the area of rectangle. If you 'unroll' a cylinder you have a shape of a rectangle, similar to a sheet of paper. The width of the rectangle will be the height of the cylinder and the length of the rectangle will be the circumference of the cylinder end.So, Area = length * widthwhere, width = height of cylinder & length = circumference of cylinder end = PI*(Diameter of cylinder)Therefore,surface area of a cylinder = (PI)*(diameter of cylinder)*(height of cylinder)Hope that helps!