Mathematical modelling question

1. Mar 23, 2006

lektor

Hey,

So, In a question about finding volume in a dome we were

Given that V = pi.k(k^2/r - k^2/3r^3 - r/8)
And K = m/2pi.p.t

Firstly we are asked to obtain an expression for the value of r that maximises the volume of air and rearrange to obtain an equation of the form ar^4 + br^2 + c = 0

V' => r^4/8 + kr^2 - k^2 = 0

So far im confident that is correct, but next it asks you to solve the equation for r^2 and hence find r, approximate squareroot of 96 to be 10.

Therefore pi^2 = 10

and substituting the value of k into this equation i obtained,

r^4/8 + mr^2/2pi.p.t - m^2/4pi^2.p^2.t^2 = 0

That is where i get stuck and i hope someone can help me out, thnx :\

2. Mar 23, 2006

HallsofIvy

Staff Emeritus
Is that $V= \pi k(\frac{k^2}{r}-\frac{k^2}{3r^3}- \frac{r}{8}$ and $k= \frac{m}{2\pi pt}$? If you don't use LaTex, use lots of parentheses. Also do not use "k" and "K" to mean the same thing.

What?? Not the $\pi$ I know! "Approximate square root of 96 to be 10"? Why???

You were told to solve for r2 first- use the quadratic formula. That's fairly straight forward and gives a relatively simple formula for r2. Since you still have unknowns m, p, t in the formula, I see no reason to "approximate" $\pi$ by 10.

3. Mar 23, 2006

HallsofIvy

Staff Emeritus
Is that $V= \pi k(\frac{k^2}{r}-\frac{k^2}{3r^3}- \frac{r}{8}$ and $k= \frac{m}{2\pi pt}$? If you don't use LaTex, use lots of parentheses. Also do not use "k" and "K" to mean the same thing.

What?? Not the $\pi$ I know! "Approximate square root of 96 to be 10"? Why???

You were told to solve for r2 first- use the quadratic formula that gives a fairly straight forward expression for r. Since you still have unknowns m, p, t, I see no reason for "approximating" $\pi$ by 10. You aren't going to get a numerical answer anyway.