Math Is Fun Forum

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

A very difficult Volume problem- need help

A right cylinder with radius r and height h. company wants to make a right cylindrical can that hold 500 cm³ of juice. assume thickness of the materical is negligible.
derive a function A(r) that represents the surface area of the can in terms of the radius,r, of its base.
show intercepts, extrema and asymptotic behavior of the function over the set of real numbers sketch graph.
state any restriction on the domain of the function so that it represents the physical model of the can.
find dimension of the can to the nearest tenth of cm.
find r=?
h=?
use differentiation

Last edited by lakeheadca (2010-01-31 21:55:33)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi lakeheadca;

I don't know what you need help on because you have not shown any work at all. I will try to start you off:

derive a function A(r) that represents the surface area of the can in terms of the radius,r, of its base.

You want A = f(r), let's try this:

1) Total Surface Area = TSA = A = 2B + hC where B is the area of the base and h is the height and C is the circumference of the base.

2) Lateral Surface Area = LSA = h * C . I guess this area does not include the 2 lids.

3) V = B * h = π r^2 h

I assume you need the entire surface area ( lids included ) so we use the TSA.

Now we have A = f(r,h) this ought to be good enough but we can eliminate h. To do this use equation 3.

V = B * h substituting.

Substituting h back in 4.

Now you have A = f(r), the first part of your question.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

Re: A very difficult Volume problem- need help

You are great. Thank you so much!  :-)

Last edited by lakeheadca (2010-02-11 20:46:14)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi;

Whoa,whoa! Your getting ahead of me and yourself. I have only solved the tiniest portion of that problem.

derive a function A(r) that represents the surface area of the can in terms of the radius,r, of its base.

I did the above and maybe it might be actually be right. How about the rest of it?

show intercepts, extrema and asymptotic behavior of the function over the set of real numbers sketch graph.
state any restriction on the domain of the function so that it represents the physical model of the can.
find dimension of the can to the nearest tenth of cm.
find r=?
h=?
use differentiation

What have you done on that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi lakeheadca;

You are very intelligent.

Yikes, have you seen my stuff! Even my mother didn't buy into that. Anyway, show me what you have done if anything. To avoid errors please repost your new questions and I will try.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Looks OK. What are we going to work on next?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi lakeheadca;

I am not sure I am following you. Here are the formulas for a rectangular prism:

V=l*w*h

A = 2(w*h + l*w + l*h )

What else do you need?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

Re: A very difficult Volume problem- need help

Is it possible that
find L,W, H, if volume of rectangular prism is 500cm³,
I am trying to find this answer. calculus seems doesn't help. I am going to ask my teachers.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi lakeheadca;

What do you want them solved in terms of?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

Re: A very difficult Volume problem- need help

I want to find all dimensions using calculus only volume is known.
I t was state exam question

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A very difficult Volume problem- need help

Hi;

I can only solve for them in terms of each other.

l = 500 / ( w * h )

w = 500 / ( l * h )

h = 500 / ( l * w )

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.