Answer:
The cone would not the all of the ice cream fit into the cone.
Step-by-step explanation:
Geometrically speaking, the volume of the cone ([tex]V_{c}[/tex]), measured in cubic inches, is described by the following equation:
[tex]V_{c} = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Base radius, measured in inches.
[tex]h[/tex] - Height, measured in inches.
And the ice cream ball is described by the volume equation for the sphere ([tex]V_{s}[/tex]), measured in cubic inches:
[tex]V_{s} = \frac{4\pi}{3} \cdot R^{3}[/tex] (2)
Where [tex]R[/tex] is the radius of the ice cream ball, measured in inches.
In this case, the ice cream will fit into the cone if and only if [tex]V_{s} \le V_{c}[/tex]. That is:
[tex]\frac{4\pi}{3}\cdot R^{3} \le \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]
[tex]4\cdot R^{3} \le r^{2}\cdot h[/tex]
If we know that [tex]r = 0.875\,in[/tex], [tex]h = 4\,in[/tex] and [tex]R = 1.25\,in[/tex], then the inequation is:
[tex]4\cdot (1.25\,in)^{3}\le (0.875\,in)^{2}\cdot (4\,in)[/tex]
[tex]6.25\,in^{3}\le 3.063\,in^{3}[/tex] (CRASH!)
Which leads to an absurd. Hence, the cone would not the all of the ice cream fit into the cone.
