If the cooler volume is represented by the cone, we can calculate the volume as:
where the radius is r = 4 cm and the height is h = 7.46 cm.
We can replace with the values and calculate:
![\begin{gathered} V=(1)/(3)\pi r^2h \\ V=(1)/(3)\pi\cdot4^2\cdot7.46 \\ V=(1)/(3)\pi\cdot16\cdot7.46 \\ V\approx125\operatorname{cm}^3 \end{gathered}]()
One cup is equal to 237 cm³, so we can calculate the volume as:
![V=125\operatorname{cm}^3\cdot\frac{1\text{ cup}}{237\operatorname{cm}^3}\approx0.53\text{ cups}]()
Answer: The cone will only fill 0.53 cups of water.