Question
A large conical tank is positioned so that its vertex is pointed downward. Water drains out from a hole at the vertex. As the water
A large conical tank is positioned so that its vertex is pointed downward. Water drains out from a hole at the vertex. As the water drains, the height of the water (measured from the vertex to the top surface) is always twice the radius of the water's surface.The formula for thevolume of a cone is: V=1/3pir^2 a. Draw and label a diagram of the situation, defining any variablesthat you use. b. Write a formula that gives the cone's volume in terms of its radius, using no other variables. c. Using variable "t" to represent the time aspect of these changes, what rate of change notation can we use for how the volume changes with respect to time and how the radius changes with respect to time? (notationfor the two quantities only, not an equation)Volume's rate of change: __________Radius' rate of change: ___________ d. Starting from the original quantity relation in (b), determine the equation that relates their rates of change with respect to time, that is, "find the related rates equation".
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