Related Rates: Adjustable Cone with dV/dt Constant

[color=#cc0000][b]Students:[/b][/color][br][br]The applet above illustrates a cone that is being filled with [color=#ff7700][b]orange soda[/b][/color].[br]In this applet, the rate of change of volume with respect to time, [math]\frac{dV}{dt}[/math], remains constant.[br]Once you click the [b]Fill Cone[/b] button, you'll see the first 8 seconds of action. [br] [br]You can enter any fill rate in the [b]Fill Rate input-box[/b] from 0 [math]\frac{cm^3}{sec}[/math] to 5 [math]\frac{cm^3}{sec}[/math]. [br][br]You can also alter the height to radius ratio of the right-circular cone into which you're pouring the [color=#ff7700][b]orange soda[/b][/color]. Enter this value in the [b]Enter h:r Ratio[/b] [b]input-box[/b]. (You can enter any ratio value [i]k[/i] > 0 but less than or equal to 5.) [br][br]If you want to find approximate values of [math]\frac{dh}{dt}[/math] and [math]\frac{dr}{dt}[/math] [color=#9900ff]when the height of the[/color] [color=#ff7700][b]orange soda-cone[/b][/color] [color=#9900ff]is a certain value, simply enter this value in the [b]Enter Height (cm) input-box[/b][/color]. [color=#9900ff](The maximum possible height you can enter in this applet is shown below this box.) Then, enter the displayed [/color][i][color=#9900ff]t[/color]-[/i][color=#9900ff]value into the [/color][b]Enter time (sec) input-box. [br][/b][br][color=#cc0000][b]How do results from this applet compare with the exact value(s) you obtained when using implicit differentiation to solve such a problem within this context? [/b][/color]

Information: Related Rates: Adjustable Cone with dV/dt Constant