Answer:
The wax will fill the mold a bit more than halfway.
Step-by-step explanation:
The volume of a sphere with radius [tex]r[/tex] is:
[tex]V = \displaystyle \frac{4}{3}\pi\, r^3[/tex].
The radius of this sphere of wax is [tex]2\;\rm in[/tex]; Its volume would be:
[tex]V(\text{sphere}) = \displaystyle \frac{4}{3}\pi \, r^3 = \frac{4}{3}\pi\times (2\; \rm in)^3 \approx 33.5\; \rm in^3[/tex].
Assume that the wax here does not evaporate, combust, or otherwise disappear. [tex]V(\text{wax}) = V(\text{sphere}) \approx 33.5\; \rm in^3[/tex].
The volume of a rectangular prism is equal to [tex]\text{Width} \times \text{Depth}\times \text{Height}[/tex].
For this mold with a rectangular prism shape:
[tex]V(\text{mold}) = (2\; \rm in) \times (5\; \rm in) \times (5\; \rm in) = 50\; \rm in^3[/tex].
Half of that would be:
[tex]\displaystyle \frac{1}{2}\,V(\text{mold}) = \frac{1}{2}\times 50\; \rm in^3 = 25\; \rm in^3[/tex].
Compare these two volumes to the volume of wax available:
[tex]\displaystyle \frac{1}{2}\, V(\text{mold}) < V(\text{wax}) < V(\text{mold})[/tex].
In other words, the wax will fill the mold a bit more than halfway, but not completely.
