# How to discover the dimensions of a sphere, from specific dimensions of a cylinder?

In my search for a mathematical solution for a home project I have become more interested in the process of the math. I have found discussions about finding cylinders within a sphere but nothing yet to help me the other way around

I have a cylinder, dimensions;
Length = 360mm
Circumference = 205mm

I wish to turn it into a sphere, using the cylinder as a frame. I imagine there is a formula for this and would love to be educated in this matter.

EDIT I realise I may mean "Orb" in place of sphere, as I suppose that a perfect circle is probably impossible? I mean to create as near a sphere as possible? I don't know how to word this succinctly and precisely.

If you want to circumscribe a sphere around a cylinder of height $h$ and radius $r$, you can draw a right triangle with one corner at the center of the cylinder, the right angle at the center of one end of the cylinder, and the other corner on the circumference of the end of the cylinder. Calling the hypotenuse of the triangle $R$, we have $R^2=(\frac h2)^2+r^2$ and $R$ is the radius of the sphere. For your numbers, $r=\frac {205}{2\pi}\approx 32.63$, so $R=\sqrt{32.63^2+180^2}\approx 182.94$