Rate related problem with irregular cone and and time delay

In summary, the problem is asking for the rate of change of the height of a water glass that is being filled at a rate of 50 cm^3/min. The glass has a diameter of 10 cm at the top and 6 cm at the bottom, and a height of 20 cm. The given equation V=1/3(3.14) r^2h is used to calculate the volume of a proper cone, but since the glass is not a proper cone, the formula V=1/3(3.14)(R^2H-r^2h) may be used. However, the presence of the 6 cm diameter at the bottom makes it difficult to solve for the rate of change at
  • #1
FiveAlive
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A water glass (10 cm diameter at the top, 6 cm diameter at the bottom, 20 cm in height) is being filled at a rate of 50 cm^3/min. Find the rate of change of the height of the water after 5 seconds.

V=1/3(3.14) r^2h

I'm a little unsure how to approach this problem for two reasons. A) The glass is not a 'proper' cone shape(it has a 'flat' bottom of 6cm), in the problems I have been solving dealing with cones there has been only one radius to deal with. B) The problem is asking for the rate of change after a period of time. In most problems I have been asked to solve for some variable in the equation( ie ...find the rate of change after a certain height has been reached in the container)

Any suggestions would be appreciated.
 
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  • #2
Update: So I've been looking at my rates of change according to height (at 1 cm, 2 cm, 3 cm ect) and I'd be able to solve it if the cone didn't have a 6 cm diameter. I am still unsure how to tackle this issue.
 
  • #3
Update: Still a little unsure how to resolve the time issue of this problem however I believe I would use the formula V=1/3(3.14)(R^2H-r^2h) to solve for my irregular cone. Am I on the right track?
 

1. What is a rate related problem with an irregular cone?

A rate related problem with an irregular cone is a mathematical problem that involves determining the rate at which a substance is flowing or changing in an irregular cone-shaped object. This can be a challenging problem to solve because the shape of the cone is not consistent, making it difficult to use traditional mathematical equations.

2. How is time delay related to an irregular cone?

Time delay is related to an irregular cone because it takes longer for a substance to flow through an irregular cone compared to a regular cone with a consistent shape. This is due to the varying distances that the substance must travel in an irregular cone, which can cause delays in the rate of flow.

3. What factors can affect the rate of flow in an irregular cone?

There are several factors that can affect the rate of flow in an irregular cone, including the shape and size of the cone, the viscosity of the substance, and any obstructions or blockages within the cone. These factors can cause variations in the rate of flow and make it challenging to accurately calculate.

4. How can we solve rate related problems with an irregular cone?

To solve rate related problems with an irregular cone, we can use mathematical techniques such as calculus or numerical methods to approximate the rate of flow. This involves breaking down the cone into smaller, more manageable sections and using equations to estimate the rate of flow in each section. The results can then be combined to determine the overall rate of flow.

5. What real-world applications involve rate related problems with an irregular cone?

Rate related problems with an irregular cone can be found in various fields, such as fluid mechanics, engineering, and physics. For example, determining the rate of flow of water through a funnel with an uneven or irregular shape, or calculating the rate of change of temperature in an irregularly shaped container. These problems are essential in understanding and predicting the behavior of fluids in complex systems.

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