(Solved): 5. The volume of a right circular cone is \( V=\frac{1}{3} \pi r^{2} h \), where \( r \) is the rad ...

5. The volume of a right circular cone is \( V=\frac{1}{3} \pi r^{2} h \), where \( r \) is the radius and \( h \) is the height. (a) Find the rate of change of the volume with respect to the height if the radius is constant, \( v^{\prime}(h) \) (b) Find the rate of change of the volume with respect to the radius if the height is constant, \( V^{\prime}(r) \) [1 point] (c) Find the rate of change of the volume with respect to time if both \( r \) and \( h \) are changing variables also, \( \frac{d V}{d t} \) [2 points]