Answer
No the vase could not be made out of platinum.
Work Step by Step
Using the formula for density: $Density = \frac{Mass}{Volume}$, we can find the density of the vase to be $Denisty = \frac{157 grams}{18.65 mL} = 8.418 g/mL$ and then using the conversion factor of $1 mL = 1 cm^{3}$, the density of the vase is 8.418 g/cm^3. Therefore this device could not be solid platinum which has a density of 21.45 g/cm^3.
