(Solved): (6 pts) Gravel is dumped from a conveyor belt at a rate of \( 10 \mathrm{ft}^{3} / \mathrm{min} \) ...

(6 pts) Gravel is dumped from a conveyor belt at a rate of \( 10 \mathrm{ft}^{3} / \mathrm{min} \) and its coarseness is such that it forms a pile in the shape of a cone whose base diameter is always approximately three times of the height. How fast is the height of the pile increasing when the pile is \( 15 f t \) high? (Hint: The formula for the volume of a cone is \( V=\frac{1}{3} \pi r^{2} h \). 2. (6 pts) A man starts walking north at \( 4 \mathrm{f} t / \mathrm{s} \) from a point P. Five minutes later a woman starts walking south at \( 5 \mathrm{ft} / \mathrm{s} \) from a point \( 500 \mathrm{f} t \) due east of \( P \). At what rate are the people moving apart \( 15 \mathrm{~m} \) after the woman starts walking?