Let V be the volume of the cone. What is the objective function in terms of the height of the cone, h ? \( \mathrm{V}=\frac{\pi}{3}\left(225 \mathrm{~h}-\mathrm{h}^{3}\right) \) (Type an expression. Type an exact answer, using \( \pi \) as needed.) The interval of interest of the objective function is \( [0,225] \). (Simplify your answer. Type your answer in interval notation.)

To express the volume \( V \) as a function of the height \( h \), we start with the given formula: \[ V = \frac{\pi}{3} (225h - h^3) \] This means that the objective function \( V(h) \) in terms of height \( h \) is: \[ V(h) = \frac{\pi}{3} (225h - h^3) \] Now, regarding the interval of interest for this function, since \( h \) represents the height of the cone, it must always lie within practical limits. Given the problem constraints, the interval in which we are analyzing the function is: \[ [0, 225] \]