Question

A sphere has a volume of 16mm². If it is recast into a cylinder, how many whole number radius and height value combinations are possible.​

Answer 1

Answer:

Sure simply set the height to vπ and the radius of the base to 1 where v is the required volume.

If you are asking if it is possible to set an actual physical body to a volume of a whole number, here you are limited by the universe. According to our understanding and current technological ability we are limited in measuring and shaping physical objects to at least the radius of an atom and most times to much less exact dimensions. An atom is about 10−10meter in diameter. That is under ideal conditions and we will have to control all physical conditins of the object and its environment (temperature, physical composition, dimensions, gravity, atmosphere, materials in contact with it, …). The largest objects we are able to manufacture in one shaping cycle are on the order of 10 meter. So the most exact dimensions of a single object we are conceivably able at this time to manufacture ar 11 orders of magnitude, this is of course highly improbable since the cost will be prohibitively high (a sphere of pure silicon the diameter of about 10cm with a dimentional precision of single atoms of silicon cost in the millions of dollars to manufacture recently, and took 10s of years to manufacture, that includes the development of techniques to manufacture and measure to this exact dimensions, World's Roundest Object! )

So since we can be exact in measurement of physical objects to about 11 orders of magnitude we can’t be more exact in measuring volume.