The problem involves an inverted right circular cone collecting water at a steady rate, with specific questions regarding the depth of water after a set time and the rate of increase of that depth. The subject area includes geometry and calculus, particularly related to volume and rates of change.
The discussion is exploring the definitions and relationships between the variables involved. Some participants have provided guidance on reviewing the formula for the volume of a cone and the physical meaning of depth in this context. There is an ongoing examination of the assumptions made regarding the problem setup.
Participants note potential confusion regarding the units of measurement and the definitions of depth versus volume, which are critical to understanding the problem. There is an emphasis on ensuring clarity in the physical interpretation of the quantities involved.
.. which would imply a depth of what, 216 cm3? Anything strike you as odd about that?lionely said:All I know is that dV/dt = 18cm3/min
so shouldn't the depth after 12 mins be 12 * dv/dt?
No, I meant depth measured in cm3 (!)lionely said:Well yeah that is way too much :S
The depth of the water is the height of the surface measured from the point of the cone. So it's a distance, not a volume, not a rate. dh/dt would be the rate of change of the depth.lionely said:Depth would be dh/dt, h being that height