I read the examples on the page, but none of them were like my one.

X

Please help me solve a rate of change problem about a conical tank wit vertex down. i dont know the equation i have to use

Relevant page
<a href="/applications-differentiation/4-related-rates.php">4. Related Rates</a>
What I've done so far
I read the examples on the page, but none of them were like my one.

Hello Ana
You will need to provide more details before I can help you.
You may get some inspiration from this page, which is also talking about a conical tank:
<a href="/functions-and-graphs/4-graph-of-function.php">4. The Graph of a Function</a>
(go to the bottom of the page.)
Regards

Hint 1: What is the formula for the volume of a cone?

Hint 2: What is the rate of flow of the water?

X

You need to show us your attempts at the problem.
Did you look at that page I suggested?
<b>Hint 1: </b> What is the formula for the volume of a cone?
<b>Hint 2: </b> What is the rate of flow of the water?

I did look at that example, but it says r = h and my question does not have that. So I got stuck.

Anyway, volume of a cone is pir2h/3

The question doesn't say what the water flow rate is.

X

I did look at that example, but it says r = h and my question does not have that. So I got stuck.
Anyway, volume of a cone is pir2h/3
The question doesn't say what the water flow rate is.

I encourage you to use the math input system, so we can read your answer more easily.

You just need to put the following in between back ticks,

V = (pi r^2 h)/2

So it looks like this:

`V=(pi r^2 h)/3`

You're right - the question doesn't give us a number for the flow rate, but we can just give it a letter, say `f` and assume it is constant at liters per minute, say.

Hint 3: How long will it take the water to flow out?

Hint 4: How do you find the rate of change of the volume?

X

I encourage you to use the math input system, so we can read your answer more easily.
You just need to put the following in between back ticks,
<code>V = (pi r^2 h)/2</code>
So it looks like this:
`V=(pi r^2 h)/3`
You're right - the question doesn't give us a number for the flow rate, but we can just give it a letter, say `f` and assume it is constant at liters per minute, say.
<b>Hint 3: </b> How long will it take the water to flow out?
<b>Hint 4: </b> How do you find the rate of change of the volume?

`(dV)/(dt) = 3(0.03 pi h^2)(dh)/(dt)` `=0.09 pi h^2(dh)/(dt)`

Where do we use `f`?

X

Radius is 1.5 m and height is 5 m, so
`r/h = 1.5/5 = 0.3`
So `r = 0.3h`
So now
`V = (pi r^2 h)/3 ` `= (pi (0.3h)^2 h)/3 ` `= 0.03 pi h^3`
I see it now
`(dV)/(dt) = 3(0.03 pi h^2)(dh)/(dt)` `=0.09 pi h^2(dh)/(dt)`
Where do we use `f`?

Well, `f` is just the rate of flow, so it's equal to the change in volume of the water. So we have

`f=0.09 pi h^2(dh)/(dt)`

Can you get the expression of the rate of change of the height now?

X

Well, `f` is just the rate of flow, so it's equal to the change in volume of the water. So we have
`f=0.09 pi h^2(dh)/(dt)`
Can you get the expression of the rate of change of the height now?

Wow, I have the same problem with my class. <a href="https://cardeaconcrete.com/van-nuys-concrete-contractors/">Van Nuys Concrete Contractors - Cardea Concrete</a>

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