I have no idea what to do: Water is being drained from a container which has the shape of....

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hellolo

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Hello, I have no idea what to do with this question. I would appreciate some help, thanks!​

Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
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hellolo said:
Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
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Hint 1: What is the formula for the volume of a right circular cone in terms of the base area and the height?

Hint 2: Take the derivative of both sides of this. You can find the surface area from the height.

Give it a try and post back if you have problems.

-Dan
 
hellolo said:
Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
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Is it assumed that the water is drained at a constant volume rate?
 
hellolo said:
Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
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inverted right circular cone has a volume of V= (pi*r^2*h)/3

radius of 6.00 inches at the top translates to r=6in

a height of 10.0 inches from bottom to top translates to h=10in

At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec translate to when h = 8in, dh/dt = 0.9in/sec

Find the rate at which water is being drained from the container which translates to find dV/dt.

The variables that come up are r, h, and V. You can find a relationship, using similar triangles, between h and r--that is you can eliminate r or h. Since they tell you about dh/dt, you should eliminate r.

See what you can do with this.
 
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blamocur said:
Is it assumed that the water is drained at a constant volume rate?
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That information will be determined after you calculate dv/dt. If dv/dt involve h then..., if dv/dt does not involve h then ....
To OP. Which is true? That is, is dv/dt a constant thought the entire process or not?
 
Steven G said:
That information will be determined after you calculate dv/dt. If dv/dt involve h then..., if dv/dt does not involve h then ....
To OP. Which is true? That is, is dv/dt a constant thought the entire process or not?
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I don't think it matters, especially if we take the question, ...
hellolo said:
Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
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... to mean "find the rate at that instant". In particular, we aren't told that the water level is falling at a constant rate.
 
hellolo said:
Hello, I have no idea what to do with this question. I would appreciate some help, thanks!
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When you say that you "have no idea what to do with this question", are you saying that you first are needing lesson instruction on how to work with related rates? Or do you need lessons starting back with derivatives? (If you were in a calculus class, all the necessary background information would have been provided, complete with worked examples of how this sort of exercise works, is why I'm asking.)

Please be specific. Thank you!

Eliz.
 
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