# Another Math WordProblem

• Feb 10th 2011, 01:34 PM
thelensboss
Another Math WordProblem
Stewart Cannery will package tomato juice in a 2L(2000 cubic centimeters) cylindrical can. Find the radius and height if the can is to have a surface area that is less than 1000 square centimeters.
(Hint: Use a rational Inequality on your calculator)
• Feb 10th 2011, 01:47 PM
pickslides
Consider the following equations

$\displaystyle \displaystyle 2000= \pi r^2h$

and

$\displaystyle \displaystyle 2\pi r (r+h)<1000$
• Feb 10th 2011, 02:41 PM
thelensboss
How to find height and radius now?
• Feb 10th 2011, 02:48 PM
skeeter
Quote:

Originally Posted by thelensboss
How to find height and radius now?

$\displaystyle h = \dfrac{2000}{\pi r^2}$

sub this expression for h in the inequality provided by pickslides ... solve for r
• Feb 10th 2011, 03:28 PM
thelensboss
I got 2(pi)(r^3)< (1000(r-4))???
tell me how to get the answer using the graphing calculator plesae thanks
• Feb 10th 2011, 05:15 PM
skeeter
Quote:

Originally Posted by thelensboss
I got 2(pi)(r^3)< (1000(r-4))???
$\displaystyle 2\pi r(r+h) < 1000$
$\displaystyle 2\pi r \left(r + \dfrac{2000}{\pi r^2}\right) < 1000$
$\displaystyle 2\pi r^2 + \dfrac{4000}{r} < 1000$
$\displaystyle 0 < 1000 - 2\pi r^2 - \dfrac{4000}{r}$
$\displaystyle 0 < 500 - \pi r^2 - \dfrac{2000}{r}$