If the volume of a cylinder is given and the diameter equals the height how do you find the height?

Answer 1

height = diameter = 2 x radius

volume_cylinder = π x radius2 x height

= π x radius2 x (2 x radius)

= 2 x π x radius3

⇒ radius = 3√(volume_cylinder/(2 x π))

⇒ height = diameter

= 2 x radius

= 2 x 3√(volume_cylinder/(2 x π))

= 3√((4 x volume_cylinder)/π)