The concepts required to solve this problem are those related to density, as a function of mass and volume. In turn, we will use the geometric concept defined for the volume.
The relationship between volume, density and mass is given under the function

Here,
m = Mass
V = Velocity
Rearranging for the Volume,

With our information the volume is


Now the volume of sphere is expressed as

Here r is the radius of Sphere, then rearranging to find the radius we have
![r = \sqrt[3]{\frac{3V}{4\pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%7D)
![r = \sqrt[3]{\frac{3(3.0769*10^{-3})}{4\pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3%283.0769%2A10%5E%7B-3%7D%29%7D%7B4%5Cpi%7D%7D)

Therefore the radius of a sphere made of this material that has a critical mass is 9.02cm