Question 193537
here is a URL for volume --> http://math.about.com/od/formulas/ss/surfaceareavol.htm

Let's think about this first.
We have a sphere that will sink in the water.
The cylinder is wide enough to contain the sphere. (one could argue that a sphere with radius 10 won't fit into a cylinder with radius 10. But we will let that one go for now)

When we drop the sphere into the cylinder of water, it sinks to the bottom.

How much water is displaced by the sphere we dropped in?

The volume of a sphere is given by {{{V = 4*pi*r^3/3}}}

So we know how much water is displaced.

Now that we know the amount of water that 'moved', and we know the container holding that water is a right circular cylinder, all we need to know is the formula for the volume of such a cylinder.

{{{V = pi*r^2 * h }}}

Now we can equate those two volumes and solve for h
{{{4 *pi * r^3 / 3 = pi * r^2 * h }}}
{{{4 * r / 3 = h }}}

We are told r = 10 , so that yields {{{h = 40/3}}} = {{{13.33}}} centimeters