Volume & Rate of Oil in Underground Tank ABCDEFGH

In summary, an underground oil storage tank ABCDEFGH is part of an inverted square pyarmid, as shown in the diagram. The complete pyramid has asquare base of side 12 m and height 18 m. The depth of the tank is 12 m. When the depth of oil in the tank is h meters, show that the volume vm^3 is given by V=4/27(h+6)^3 -32. The oil is being added to the tank at the constant rate of 4.5m^3 s^-1 at the moment when the depth of oil is 8 m. Find the rate at which the depth is increasing.
  • #1
momo89
4
0
An underground oil storage tank ABCDEFGH is part of an inverted square pyarmid, as shown in the diagram. the complete pyramid has asquare base of side 12 m and height 18 m.the depth of the tank is 12 m.

http://haniny.com/haniny/Square_pyramid.gif

when the depth of oil in the tank is h meters,show that the volume vm^3 is given by

V=4/27(h+6)^3 -32

oil is being added to the tank at the constant rate of 4.5m^3 s^-1 at the moment when the depth of oil is 8 m.Find the rate at which the depth is increasing

What is the solution? please:rolleyes:
 
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  • #2
First this has absolutely nothing to do with differential equations!

Second, it looks to me like homework so I am going to move this to the "homework: Calculus and Beyond" section.

Finally, you must show some attempt to do the problem yourself so that we can see what kind of help you need.
 
  • #3
What is the difference between the "height" of the pyramid and the "depth" of the tank?
 
  • #4
HallsofIvy said:
What is the difference between the "height" of the pyramid and the "depth" of the tank?

i do not know:rolleyes:

i need the solution for the question!

please
 
  • #5
HallsofIvy said:
First this has absolutely nothing to do with differential equations!QUOTE]


i do not think so:rolleyes:
 
  • #6
momo89 said:
i do not know:rolleyes:

i need the solution for the question!

please

So... that mean, you don't need help? What you need is a complete solution, eh?

Do you find it a little bit unfair for us all just to just sit, and solve the problems for you?? No, we are not paid to do that! We are here to help you, and not to feed you with complete solutions.

Now, take some time off to read the sticky on top of this forum please:

The new version can be found https://www.physicsforums.com/showthread.php?t=94383".

I, myself, prefer the old one, you can read it https://www.physicsforums.com/showthread.php?t=28".

Then, please collaborate. Show some work!
 
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  • #7
VietDao29 said:
So... that mean, you don't need help? What you need is a complete solution, eh?

Do you find it a little bit unfair for us all just to just sit, and solve the problems for you?? No, we are not paid to do that! We are here to help you, and not to feed you with complete solutions.

Now, take some time off to read the sticky on top of this forum please:

The new version can be found https://www.physicsforums.com/showthread.php?t=94383".

I, myself, prefer the old one, you can read it https://www.physicsforums.com/showthread.php?t=28".

Then, please collaborate. Show some work!


thank you very much:confused:
 
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  • #8
You apparently are unable to even state the problem correctly. You said "the height of the pyramid is 18 m" and "the depth of the tank is 12 m" but do not know what those mean. I strongly suspect that the "6" in "(h+6)" comes from the difference between the height of the pyramid and the depth of the tank, but I can't be sure when I don't know what they correspond to on your picture.

Oh, and when you say "i do not think so" to my statement that this problem has nothing to do with differential equations. If you believe it does, I would like to see what kind of differential equation is involved!
 
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  • #9
Couldn't you make a differential equation because the rate at which the depth increases decreases as the depth goes up? The volume is increasing at a constant rate. The depth is not.
 

FAQ: Volume & Rate of Oil in Underground Tank ABCDEFGH

1. What is the purpose of measuring the volume and rate of oil in underground tank ABCDEFGH?

The volume and rate of oil in an underground tank is an important measurement for several reasons. It helps determine how much oil is available for use, how quickly it is being used, and when it needs to be refilled. This information is crucial for managing and maintaining the oil supply and preventing unexpected shortages or overflows.

2. How is the volume of oil in underground tank ABCDEFGH measured?

The volume of oil in an underground tank is typically measured using a dipstick or a gauge that is inserted into the tank. These tools have markings that indicate the amount of oil in the tank. Alternatively, modern technology has also allowed for the use of ultrasonic sensors or radar level gauges to measure the volume of oil in a tank.

3. What factors can affect the rate of oil in underground tank ABCDEFGH?

The rate of oil in an underground tank can be affected by a variety of factors. These may include the size and capacity of the tank, the temperature and viscosity of the oil, the rate of consumption or usage, and any potential leaks or spills.

4. How often should the volume and rate of oil in underground tank ABCDEFGH be checked?

The frequency of measuring the volume and rate of oil in an underground tank may vary depending on the specific tank and its usage. However, it is recommended to check these measurements at least once a month to ensure proper management and maintenance of the oil supply.

5. What are the potential consequences of not monitoring the volume and rate of oil in underground tank ABCDEFGH?

Failing to monitor the volume and rate of oil in an underground tank can lead to a variety of consequences. These may include unexpected shortages or overflows, which can result in disruptions to operations and additional costs for refilling the tank. It can also pose environmental risks if leaks or spills go undetected. Therefore, regular monitoring is essential for the safe and efficient use of oil in underground tanks.

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