1. ## 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)

2. Consider the following equations

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

and

$\displaystyle 2\pi r (r+h)<1000$

3. How to find height and radius now?

4. Originally Posted by thelensboss
How to find height and radius now?
$h = \dfrac{2000}{\pi r^2}$

sub this expression for h in the inequality provided by pickslides ... solve for r

5. I got 2(pi)(r^3)< (1000(r-4))???
tell me how to get the answer using the graphing calculator plesae thanks

6. Originally Posted by thelensboss
I got 2(pi)(r^3)< (1000(r-4))???
tell me how to get the answer using the graphing calculator plesae thanks
$2\pi r(r+h) < 1000$

$2\pi r \left(r + \dfrac{2000}{\pi r^2}\right) < 1000$

$2\pi r^2 + \dfrac{4000}{r} < 1000$

$0 < 1000 - 2\pi r^2 - \dfrac{4000}{r}$

$0 < 500 - \pi r^2 - \dfrac{2000}{r}$

graph the right side of the inequality using x to represent r ... look for where the graph is greater than 0 (i.e. above the x-axis) ... you'll have a range of choices for r. once you pick a value for r, calculate the corresponding value for h that yields the fixed volume.