The answer is: The diameter is 4 centimeters.
The explanation is shown below:
1. The volume of the cylinder is:
[tex]Vc=r^{2}h \pi[/tex]
Where [tex]r[/tex] is the radius ([tex]r=\frac{16cm}{2}=8cm[/tex]) and [tex]h[/tex] is the height ([tex]h=2cm[/tex]).
Then:
[tex]Vc=(8cm)^{2}}(2cm)\pi\\Vc=128\pi[/tex]
2. The total volume of the 12 spheres is:
[tex]Vs=12(\frac{4}{3}r^{3}\pi)\\Vs=16r^{3}\pi[/tex]
3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:
[tex]Vc=Vs\\128\pi=16r^{3}\pi[/tex]
4. Now, you must solve for the radius:
[tex]r=\sqrt[3]{\frac{128\pi}{16\pi}}\\r=2cm[/tex]
5. The diameter is:
[tex]d=2r\\d=2(2cm)\\d=4cm[/tex]
