The surface area of a closed cylinder is equal to (2 times the area of the base) plus (the height times the circumference of the base)
a line segment has no area. By definition a line segment is a part of a line, thus it has no area
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.
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
Think of a paper clip as a cylinder that has been bent into a specific shape. Determine the volume of the cylinder, and you have the volume of the paper clip. So, the area of the end of the cylinder x length of the cylinder = volume of the paper clip.
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.)
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