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.
i will give you a link to a page that explains it. http://mathworld.wolfram.com/CylindricalSegment.html
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.
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 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!
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.
Area of the base of a cylinder = pi*radius2
The area for the base of a cylinder is the area of a circle. pi times radius squared.