Related Rates: Adjustable Cone with dV/dt Constant
- Tim Brzezinski
Students: The applet above illustrates a cone that is being filled with orange soda. In this applet, the rate of change of volume with respect to time, , remains constant. Once you click the Fill Cone button, you'll see the first 8 seconds of action. You can enter any fill rate in the Fill Rate input-box from 0 to 5 . You can also alter the height to radius ratio of the right-circular cone into which you're pouring the orange soda. Enter this value in the Enter h:r Ratio input-box. (You can enter any ratio value k > 0 but less than or equal to 5.) If you want to find approximate values of and when the height of the orange soda-cone is a certain value, simply enter this value in the Enter Height (cm) input-box. (The maximum possible height you can enter in this applet is shown below this box.) Then, enter the displayed t-value into the Enter time (sec) input-box. 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?