Finding Water Depth in an Inverted Cone

[lionely]

Homework Statement

An inverted right circular cone of vertical angle 120 is collecting water from a tap at a steady rate of 18∏ cm^3/min. Find
a) the depth of water after 12min,
b) rate of increase of depth at this instant

Homework Equations

The Attempt at a Solution

All I know is that dV/dt = 18cm3/min
so shouldn't the depth after 12 mins be 12 * dv/dt?

 

[haruspex]

All I know is that dV/dt = 18cm3/min
so shouldn't the depth after 12 mins be 12 * dv/dt?

.. which would imply a depth of what, 216 cm³? Anything strike you as odd about that?

 

[lionely]

Well yeah that is way too much :S

 

[haruspex]

Well yeah that is way too much :S

No, I meant depth measured in cm³ (!)

 

[lionely]

Depth would be dh/dt, h being that height

 

[vela]

That would give you units of cm/min, which isn't the units of depth. Based on your answer, I'm not sure you understand what the word depth means in the context of this problem.

Why don't you start by looking up the formula for the volume of a cone? Sketch a picture and tell us how the variables in the formula relate to the physical quantities in this problem.

 

[haruspex]

Depth would be dh/dt, h being that height

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.