Related Rates: Inverted Conical Tank Problem

In summary, water is both leaking out of and being pumped into an inverted conical tank with a height of 6m and a diameter of 4m. The water level is rising at a rate of 20cm/min when the height is 2m. Using the volume formula of a cone, the rate at which the water is being pumped into the tank can be found by setting up and solving an equation.
  • #1
suspenc3
402
0
Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank is 6m high and the diameter at the top is 4m. If the water level is rising at a rate of 20cm/min when the height of the water is 2m, find the rate at which the water is being pumped into the tank.

Its not the math I am having trouble with, its setting up the question, ca anyone help?

Thanks
 
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  • #2
I used [tex]V=1/3 \\(pi) r^2h[/tex]..and then proceeded to find [tex]V= \\(pi) r^3[/tex]..I don't really know what to do now
 
Last edited:
  • #3
What is v as a function of h?
dh/dt = 20
h = 200
dv/dt = ?

Then algebra will get you to the rate at which the water is being pumped in.
 

1. What is a simple related rates question?

A simple related rates question is a type of problem in which the rate of change of one variable depends on the rate of change of another related variable. These types of questions often involve finding the rate of change of a specific quantity at a given point in time.

2. How do I solve a simple related rates question?

To solve a simple related rates question, you first need to identify the variables involved and how they are related. Then, you can use the chain rule to express the rate of change of one variable in terms of the rate of change of another. Finally, you can plug in the given values and solve for the desired rate of change.

3. What is the chain rule?

The chain rule is a calculus rule that allows you to find the derivative of a function composed of two or more functions. In a simple related rates question, the chain rule is used to express the rate of change of one variable in terms of the rate of change of another.

4. What are some common examples of simple related rates questions?

Some common examples of simple related rates questions include problems involving the rate of change of the volume or surface area of a shape, the rate of change of the distance between two moving objects, and the rate of change of the angle of elevation or depression of an object.

5. What are some tips for solving simple related rates questions?

Some tips for solving simple related rates questions include carefully reading and understanding the problem, drawing a diagram to visualize the situation, using the chain rule correctly, and checking your solution for reasonableness. It can also be helpful to practice solving similar types of problems to improve your understanding and problem-solving skills.

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