height has to be given. or volume. volume of a cylinder is v = (pi r ^2) h or diameter times height.
Diameter = 2 * square root of {(volume / (pi * Height))} or in symbols d= 2 * (v/(pi * h))^1/2
The radius IS given, since height of hemisphere = radius of hemisphere!
Easy, you find the area of the circle (Pi X Radius squared) and then multiply it by the height. Your question asks about using the diameter...the radius is half of the diameter.
The answer depends on what information you are given: volume and radius or diameter, or surface area and radius, etc.
pi*radius2*height = volume of a cylinder height = volume divided by pi*radius2
First you have to know that the [ Volume of a cylinder = (pi) x (radius)2 x (height) ].Then you just massage that formula around to solve it for the height.Thusly:Volume = (pi) x (1/2 diameter)2 x (height)Multiply each side by 'height' :(Volume) x (height) = (pi) x (1/2 diameter)2Divide each side by 'volume' :Height = (pi) x (1/2 diameter)2/(volume) .And there you have it ... you know all of the items on the right side.
Make the height the subject of the fornula for the volume or surface area of the cylinder
Volume of a cylinder in cubic units = piradius2height
That will depend on its height which has not been given but the volume of a cylinder is pi*radius squared*height.
Divide volume by height will give you cross sectional area. The cross section of a cylinder is a circle. Area of a circle= π r2 divide your value of cross sectional area by π square root this value and multiply it by 2 that value is diameter.
Volume = pi*r2*h