Am I right about this rectangle? Cylinder is 4.5 wide, 10 high; gets wider but smaller as function of x

[Cb3rs]

So there is this cylinder with the size 4.5 (wide) x 10(high) cm. It gets wider but smaller in height as a function of x. And I have to describe it. The question is:
Describe the volume V as a function of x.

My solution is ((4.5+x)²*pi) * (10-x)

Is this possible?

 

[stapel]

So there is this cylinder with the size 4.5 (wide) x 10(high) cm.

When you say "wide", are you referring to the diameter of the cylinder?

It gets wider but smaller in height as a function of x.

I'm sorry, but I don't understand what this means?

Describe the volume V as a function of x.

There is no "x" in what you've posted. How is this variable meant to relate to anything?

My solution is ((4.5+x)²*pi) * (10-x)

Is this possible?

It's hard to say, especially since we can't see your work. Kindly please reply with clarification. Thank you!

 

[Dr.Peterson]

So there is this cylinder with the size 4.5 (wide) x 10(high) cm. It gets wider but smaller in height as a function of x. And I have to describe it. The question is:
Describe the volume V as a function of x.

My solution is ((4.5+x)²*pi) * (10-x)

Is this possible?

Please, as we ask in our submission guidelines, state the entire problem as given to you. If there is a picture, either describe it sufficiently that we can reproduce it completely, or attach an image.

Your formula will be correct if 4.5 is the radius, not the diameter (width), and if x is the amount by which it is simultaneously made shorter and the radius is increased. None of that is clear from your description.

 

[Cb3rs]

Please, as we ask in our submission guidelines, state the entire problem as given to you. If there is a picture, either describe it sufficiently that we can reproduce it completely, or attach an image.

Your formula will be correct if 4.5 is the radius, not the diameter (width), and if x is the amount by which it is simultaneously made shorter and the radius is increased. None of that is clear from your description.

Sorry, I described it as well as I could given my English skills. Yes, it is the radius.

 

[Cb3rs]

So my problem is that on the solution it is described like this:

pi * (-x³+x²+69.75*x+202.5)

What did they do here?

 

[Cb3rs]

When you say "wide", are you referring to the diameter of the cylinder?


I'm sorry, but I don't understand what this means?


There is no "x" in what you've posted. How is this variable meant to relate to anything?


It's hard to say, especially since we can't see your work. Kindly please reply with clarification. Thank you!

Sorry.
1. I mean the radius

2. If x would be for example 4, the cylinder would get 6 cm high and 13cm wide. I hope that clarified it. And I had to describe what x would change about the volume.

 

[stapel]

So my problem is that on the solution it is described like this:

pi * (-x³+x²+69.75*x+202.5)

What did they do here?

We have no way of knowing. Did they not show their steps in the solution? Also, you originally said that you need to express the volume as a function of x, so you're needing to create something of the form "V(x) = [stuff goes here]". But the "solution" is just an expression...?

 

[Dr.Peterson]

So there is this cylinder with the size 4.5 (wide) x 10(high) cm. It gets wider but smaller in height as a function of x. And I have to describe it. The question is:
Describe the volume V as a function of x.

My solution is ((4.5+x)²*pi) * (10-x)

Is this possible?

Sorry, I described it as well as I could given my English skills. Yes, it is the radius.

It's not just a matter of English skills. From what you've told us, the problem is missing information. If all you are told is that "It gets wider but smaller in height as a function of x", then you don't know WHAT functions of x the "width" (radius) and height are. You assumed that they are increasing and decreasing as LINEAR functions of x.

So my problem is that on the solution it is described like this:

pi * (-x³+x²+69.75*x+202.5)

What did they do here?

This is equivalent to what you wrote! Just expand your ((4.5+x)²*pi) * (10-x), that is, distribute, and you will get their answer. So apparently whatever the problem actually said, you interpreted it the way they intended ...

 

[Cb3rs]

[MATH][SUP] [QUOTE="Dr.Peterson, post: 450186, member: 62318"] It's not just a matter of English skills. From what you've told us, the problem is missing information. If all you are told is that "It gets wider but smaller in height as a function of x", then you don't know WHAT functions of x the "width" (radius) and height are. You assumed that they are increasing and decreasing as LINEAR functions of x. This is equivalent to what you wrote! Just expand your ((4.5+x)²*pi) * (10-x), that is, distribute, and you will get their answer. So apparently whatever the problem actually said, you interpreted it the way they intended ... [/QUOTE] Thank you for the answer, I think it helped me [/SUP][/MATH]

 

[Cb3rs]

We have no way of knowing. Did they not show their steps in the solution? Also, you originally said that you need to express the volume as a function of x, so you're needing to create something of the form "V(x) = [stuff goes here]". But the "solution" is just an expression...?

Sorry, yes it it V(x)