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So we are first trying to find the volume of a scoop which is essentially half a sphere.
A sphere's volume equation is [tex]\frac{4}{3} \pi r^{3}[/tex] but times '1/2' in this case as we only need half of it.
Since the radius of the scoop is 2cm, we get the equation:
[tex]\frac{4}{3} \pi *2^{3} *\frac{1}{2} = \frac{16}{3}\pi = 16.755[/tex]
So the volume of the scoop is 16.755 cubic centimeters.
For the cone to fill with melted ice cream and not spill, that means the volume of the scope must equal the volume of the cone.
the volume of cone = volume of half of sphere
[tex]\frac{1}{3} \pi r^{2} h = \frac{16}{3} \pi \\\frac{1}{3 } \pi 2^{2} h=\frac{16}{3} \pi \\h = 4\\\\[/tex]
The height of the cone must be 4cm to fit all the ice cream without spilling if it melts.
Hope that helps!