Lovely word problem

[trinan71]

The question is A cylindrical container for storing radioactive waste is to be constructed from lead. This container must be 6 in thick. The volume of the outside cylinder shown in the future is to be 16pi ft³.

a.) Express the height h of the inside cylinder as a function of the inside radius r. (The answer is h=16/(r+0.5)² -1 but I need to know how to get there)

B.) Show that the inside volume V(r) is given by V(r)= pi r² (16/(r+0.5)² -1) (The answer is V(r)=pi r² h, but need to know the process to find the answer)

Thank you!! I need by tomorrow morning by the way

 

[Deleted member 4993]

The question is A cylindrical container for storing radioactive waste is to be constructed from lead. This container must be 6 in thick. The volume of the outside cylinder shown in the future is to be 16pi ft³.

a.) Express the height h of the inside cylinder as a function of the inside radius r. (The answer is h=16/(r+0.5)² -1 but I need to know how to get there)

B.) Show that the inside volume V(r) is given by V(r)= pi r² (16/(r+0.5)² -1) (The answer is V(r)=pi r² h, but need to know the process to find the answer)

Thank you!! I need by tomorrow morning by the way

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[trinan71]

ok....I don't have much to start with though.

I understand the function will be h= something r². That is all I can tell you. I don't know what to do.

 

[Deleted member 4993]

I understand the function will be h= something r². That is all I can tell you. I don't know what to do.

If

the radius of the outside container is r_o → the radius of the inside cylider is r_i = r = (r_o - t)

the height of the outside container is h_o → the radius of the inside cylider is h_i = h = (h_o - 2t)

What else can you do now....

 

[JeffM]

The question is A cylindrical container for storing radioactive waste is to be constructed from lead. This container must be 6 in thick. The volume of the outside cylinder shown in the future is to be 16pi ft³.

a.) Express the height h of the inside cylinder as a function of the inside radius r. (The answer is h=16/(r+0.5)² -1 but I need to know how to get there)

B.) Show that the inside volume V(r) is given by V(r)= pi r² (16/(r+0.5)² -1) (The answer is V(r)=pi r² h, but need to know the process to find the answer)

Thank you!! I need by tomorrow morning by the way

The first thing to do in any word problem is to WRITE DOWN labels for EACH unknown. In this problem, that has already been partially done for you.

What is initially unknown:

radius of inner cylinder = r (done by the problem)

height of inner cylinder = h (done by the problem)

v = volume of inner cylinder

t = thickness of shell (done by the problem)

s = radius of outer cylinder

g = radius of outer shell

w = volume of outer cylinder

The second thing to do is to WRITE DOWN in mathematical form what are the relationships among the unknowns that are either generally known (such as the formula for the volume of a cylinder) or specified in the problem itself (such as the thickness of the shell and the volume of the outer cylinder).

You now no longer have a word problem. You have a a problem of applying mathematical tools to specified relationships.

This process will let you do any word problem.

 

[Deleted member 4993]

I understand the function will be h= something r². That is all I can tell you. I don't know what to do.

Not really ... where/how did you get that idea?

 

[trinan71]

Not really ... where/how did you get that idea?

By the wording of the problem. Word problems are my pitfall. I have never been good at piecing them together. I understand you need to label unknowns but setting up the equation/formula is difficult for me to understand.

My tutor at the college I go to could not figure this question out and recommended I come here to see if anyone could help me with it. However, this site seems to be more of "I'll give you a little hint" sort of thing instead of showing me how to attack a problem like this, maybe in a simplified way, so I can learn how to do it.

I'll come back when I have a problem that I know where to start but get stuck at a certain part.