reasons of matches between 3D-figure to graph

[shahar]

Somebody fills two jugs by water (as in the graph) in stable rate.
The graphs describe the high of the water as function of filling water.
I can see that graph I is for jug A and graph II is for jug B. I see it from geometric reason. How Can I explain the answer? Is explaining by the words that it depends on geometric properties is enough. And how can I elaborate the answer so the answer will be a perfect answer.
Thanks for helping me.

 

[Deleted member 4993]

View attachment 31175
Somebody fills two jugs by water (as in the graph) in stable rate.
The graphs describe the high of the water as function of filling water.
I can see that graph I is for jug A and graph II is for jug B. I see it from geometric reason. How Can I explain the answer? Is explaining by the words that it depends on geometric properties is enough. And how can I elaborate the answer so the answer will be a perfect answer.
Thanks for helping me.

Explanation of any phenomenon depends on the audience. The description of a moon-rise for a poet (and the moon kisses the sky - Shelly) will be different from the description for a child (a big lighted balloon).

In this case, I would derive the equation of height vs. time and describe the gradient of that function.

 

[Dr.Peterson]

View attachment 31175
Somebody fills two jugs by water (as in the graph) in stable rate.
The graphs describe the high of the water as function of filling water.
I can see that graph I is for jug A and graph II is for jug B. I see it from geometric reason. How Can I explain the answer? Is explaining by the words that it depends on geometric properties is enough. And how can I elaborate the answer so the answer will be a perfect answer.
Thanks for helping me.

Are you sure of your conclusion? Explain it to us in any way you like, formally or informally, and that can serve as a basis for your answer.

I think one of the graphs is not really accurate, for a reason I can easily explain informally. It's not easy to find the equation exactly; you'll have to look up or derive the volume of a frustum.

By the way, the graphs show height of water as a function of time, not of "filling water"; but since (as I interpret it) the rate of flow in volume per time is constant, the horizontal axis is proportional to volume of water.

 

[shahar]

Are you sure of your conclusion? Explain it to us in any way you like, formally or informally, and that can serve as a basis for your answer.

I think one of the graphs is not really accurate, for a reason I can easily explain informally. It's not easy to find the equation exactly; you'll have to look up or derive the volume of a frustum.

By the way, the graphs show height of water as a function of time, not of "filling water"; but since (as I interpret it) the rate of flow in volume per time is constant, the horizontal axis is proportional to volume of water.

The way I can explain it is by geometric property. The A jug have a property of equal size basis to every height, when the B figure is narrow in the bottom and wide in the high of its. Is it enough?

 

[Dr.Peterson]

The way I can explain it is by geometric property. The A jug have a property of equal size basis to every height, when the B figure is narrow in the bottom and wide in the high of its. Is it enough?

No. Explain how that affects the graph, particularly the rate of change of the graph (its gradient, as SK said).

 

[shahar]

No. Explain how that affects the graph, particularly the rate of change of the graph (its gradient, as SK said).

I don't know how to write the answer. Can you give me more hints or words can I use by formulate the answer?

 

[Dr.Peterson]

I don't know how to write the answer. Can you give me more hints or words can I use by formulate the answer?

When the water reaches a point where the container is wider, will the water level rise faster or slower than before? That's what I mean by rate of change, and it can be understood if you have ever seen a flood and thought about what was happening, though some calculus concepts could help.

You'll see my objection to the problem if you take this same reasoning far enough.

 

[shahar]

When the water reaches a point where the container is wider, will the water level rise faster or slower than before? That's what I mean by rate of change, and it can be understood if you have ever seen a flood and thought about what was happening, though some calculus concepts could help.

You'll see my objection to the problem if you take this same reasoning far enough.

Thanks. I think that I can answer the question.