Dispute over solution: Rates of Change. (1 Viewer)

[hayabusaboston]

Had exam today, teacher and I are having an argument over whether one of the answers to the exam was 7 or 10.5, can someone confirm which one it is please?

"Water is being poured into an upright cone shaped container with base circle having radius 3cm and height of cone 7cm, at a rate of 21 cubic centimetres per second. Find the rate at which the area of the circle part of the cone is increasing (pi tmes r^2 area) when the height of the water in the cone is 6cm.

My working:
r=(3/7)h
V=1/3.pi.r^2.h --> GAH TOO TEDIOUS TO WRITE

But I ended up with dA/dt=dV/dt times dA/dV, where dv/dt=21, and dA/dV is dA/dr times dr/dV, and I ended up with 7cm.

Another one of my teachers said he cant see anything wrong with my answer, but class teacher is saying its completely wrong. What the fuck.

Someone confirm??

 

[Emily Howard]

Re: Effing irritating dispure over marks

yer wrong bbygurl

 

[braintic]

Re: Effing irritating dispure over marks

Had exam today, teacher and I are having an argument over whether one of the answers to the exam was 7 or 10.5, can someone confirm which one it is please?

"Water is being poured into an upright cone shaped container with base circle having radius 3cm and height of cone 7cm, at a rate of 21 cubic centimetres per second. Find the rate at which the area of the circle part of the cone is increasing (pi tmes r^2 area) when the height of the water in the cone is 6cm.

My working:
r=(3/7)h
V=1/3.pi.r^2.h --> GAH TOO TEDIOUS TO WRITE

But I ended up with dA/dt=dV/dt times dA/dV, where dv/dt=21, and dA/dV is dA/dr times dr/dV, and I ended up with 7cm.

Another one of my teachers said he cant see anything wrong with my answer, but class teacher is saying its completely wrong. What the fuck.

Someone confirm??

I'd like to know what is meant by 'the area of the circle part of the cone' and by 'an upright cone'.
To me 'upright' gives no indication of whether the base is above or below the apex. And how is any part of the cone itself associated with a rate of change?

If you have copied that correctly, then it is a very poorly worded question.

 

[RealiseNothing]

Re: Effing irritating dispure over marks

I'd like to know what is meant by 'the area of the circle part of the cone' and by 'an upright cone'.
To me 'upright' gives no indication of whether the base is above or below the apex. And how is any part of the cone itself associated with a rate of change?

If you have copied that correctly, then it is a very poorly worded question.

I was thinking the exact same thing.

 

[RealiseNothing]

Re: Effing irritating dispure over marks

But I get 7.

 

[RealiseNothing]

Re: Effing irritating dispure over marks

View attachment 28256

I'm not sure... But I think your teacher was right?

 

[egnaro315]

Re: Effing irritating dispure over marks

I got 10.5 assuming the apex is at the bottom

 

[hayabusaboston]

Re: Effing irritating dispure over marks

I'd like to know what is meant by 'the area of the circle part of the cone' and by 'an upright cone'.
To me 'upright' gives no indication of whether the base is above or below the apex. And how is any part of the cone itself associated with a rate of change?

If you have copied that correctly, then it is a very poorly worded question.

Its like filling in a bowl with water, water starts at the apex, and the circle that is the surface of the water gets bigger. FInd the rate at which this is getting bigger at h=6, with dV/dt=21

 

[braintic]

Re: Effing irritating dispure over marks

Its like filling in a bowl with water, water starts at the apex, and the circle that is the surface of the water gets bigger. FInd the rate at which this is getting bigger at h=6, with dV/dt=21

I realised that this was probably the only way of interpreting the question. But the wording did not indicate this clearly. Instead of referring to 'the circle part of the cone' (the cone itself doesn't change), it should have referred to the surface of the water. And if I was to try and interpret 'upright', I would probably imagine the only stable configuration - that is apex up.

 

[D94]

Re: Effing irritating dispure over marks

I'd like to know what is meant by 'the area of the circle part of the cone' and by 'an upright cone'.
To me 'upright' gives no indication of whether the base is above or below the apex. And how is any part of the cone itself associated with a rate of change?

If you have copied that correctly, then it is a very poorly worded question.

These questions can be "usually" visualised. What does filling a cone with water with the base at the bottom look like? That's nonsense. If it said a frustum, then your point can be well made.

 

[hayabusaboston]

Re: Effing irritating dispure over marks

SO WHAT IS ANSWER
10.5 or 7?

My teacher was like, full brunt angry when I even questioned her answer ever so politely, wanting to show her my solution she's like "NO, THATS TOTALLY WRONG, RELATING R AND H IS ALL COMPLETELY WRONG"



I love my maths teacher but today she made me fricken irritated with her adamance in 10.5

 

[braintic]

Re: Effing irritating dispure over marks

These questions can be "usually" visualised. What does filling a cone with water with the base at the bottom look like? That's nonsense. If it said a frustum, then your point can be well made.

I don't understand your objection. Why can't water be poured into an apex-up cone? There is no mention of the means by which water enters the cone (other than the fact it is being poured), and there is no mention of 'filling' the cone.

 

[Carrotsticks]

SO WHAT IS ANSWER
10.5 or 7?

My teacher was like, full brunt angry when I even questioned her answer ever so politely, wanting to show her my solution she's like "NO, THATS TOTALLY WRONG, RELATING R AND H IS ALL COMPLETELY WRONG"



I love my maths teacher but today she made me fricken irritated with her adamance in 10.5

Sent from my GT-N8010 using Tapatalk 2

 

[D94]

Re: Effing irritating dispure over marks

I don't understand your objection. Why can't water be poured into an apex-up cone? There is no mention of the means by which water enters the cone (other than the fact it is being poured), and there is no mention of 'filling' the cone.

"Poured" and "height" imply it's being filled. It's far better to assume it is being filled either from the apex or the base than a hole in the side of the cone since it doesn't explicitly say. But what does it mean to fill a cone through it's apex? An apex is a closed section of the cone. If there was a hole in the apex, it would be a frustum. It just says cone, not a conical frustum, so it clearly isn't being filled through the apex. But this is just my understanding of it.

 

[hayabusaboston]

Re: Effing irritating dispure over marks

Sent from my GT-N8010 using Tapatalk 2

OK good, if carrotsticks agrees with my result then I must be right haha.

How do I politely dispute this further with my teacher? She just so dismissively said "No its completely wrong to relate h and r" and then she just walked away. What do I do?

 

[Carrotsticks]

Re: Effing irritating dispure over marks

How do I politely dispute this further with my teacher? She just so dismissively said "No its completely wrong to relate h and r" and then she just walked away. What do I do?

Take it to the head teacher then. Her statement "No its completely wrong to relate h and r" is 'completely wrong' in itself. How else do you do those maxima/minima problems or how else do you complete those Extension 2 Volumes (non-revolution) problems?

 

[hayabusaboston]

Re: Effing irritating dispure over marks

Take it to the head teacher then. Her statement "No its completely wrong to relate h and r" is 'completely wrong' in itself. How else do you do those maxima/minima problems or how else do you complete those Extension 2 Volumes (non-revolution) problems?

I had a brief talk with head teacher about it on friday and he said he'll discuss it with my teacher. I hope he BEATS SOME SENSE INTO HER lol.

 

[Shadowless]

Yep, my bad. hayabusaboston, you were right. I think I forgot that r and h were related... somehow... .

 

[braintic]

Re: Effing irritating dispure over marks

"Poured" and "height" imply it's being filled.

Really? Rationalisation at its best.

 

[Makematics]

what im interested to know is how your teacher even got 10.5?