Question 1153242

Depends on the dimensions of the cone, specifically  the height of it.

Since dimensions are not given, we can say that if her ice cream melts of the ice cream will {{{not}}}overflow out of the cone only if  the volume of {{{2}}}ice cream scoops is same as the volume of the cone.

Assume the ice cream scoop is a sphere of radius {{{r}}} inches and then the top of the cone will also have radius {{{r}}} inches. 
Suppose the height of the cone is {{{h}}} inches. You need to find out if the volume of the {{{2}}} scoops of ice cream is equal the volume of the cone.


the volume of the {{{2}}} scoops (spheres ): 

{{{V[s]=2*(4/3)pi*r^3}}}

the volume of the cone:  

{{{V[c]=(1/3)pi*r^2*h}}}

{{{2(4/3)pi*r^3=(1/3)pi*r^2*h}}}........solve for{{{ h}}}

{{{(8/3)pi*r^3=(1/3)pi*r^2*h}}}........simplify

{{{(8/3)*r=(1/3)*h}}}

{{{h=(8/3)*r/(1/3)}}}

=> {{{h = 8r}}}

If her ice cream melts of the ice cream will {{{not}}}overflow out of the cone only if {{{h = 8r}}}.

only if {{{h = 8r}}} both volumes are same:

{{{V[s]=(8/3)pi*r^3}}}
{{{V[c]=(1/3)pi*r^2*8r=(8/3)pi*r^3}}}

  .