Sand is being dropped at the rate 10 metercube/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?

Answer 1

v = 1/3 pi r^2 (2r) = 2/3 pi r^3
at r=8,

dv/dt = 2 pi r^2 dr/dt

Now we just have to decide what "at what rate is the increasing" means