Another Math WordProblem

**thelensboss** · February 10th 2011, 01:34 PM

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)

**pickslides** · February 10th 2011, 01:47 PM

Consider the following equations

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

and

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

**thelensboss** · February 10th 2011, 02:41 PM

How to find height and radius now?

**skeeter** · February 10th 2011, 02:48 PM

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

**thelensboss** · February 10th 2011, 03:28 PM

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

**skeeter** · February 10th 2011, 05:15 PM

Originally Posted by thelensboss

I got 2(pi)(r^3)< (1000(r-4))???
Please help
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.

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