## anonymous 5 years ago It is your job to design an open-topped rectangular box with height h and a square base of side length s using 5 sheets of metal (one for the base and 4 equal ones for the sides). You are allowed to use a total of 5 square meters of metal. Let V be the volume of the box and A be the area of the box. Begin by finnding formulas for V and A in terms of s and h. Given that A = 5 and a formula for V involving ONLY s (no h's). Finally use your graphing calculator to estimate the value of s that gives the maximum volume. s is

1. anonymous

I'll write something up for you and scan it, okay?

2. anonymous

3. anonymous

You have to plug in A=5 and plot the equation, $V=\frac{s}{4}(5-s)$

4. anonymous

5. anonymous

You're being asked to find the highest point on a plot, when you punch in the formula into your calculator. The horizontal axis is s (side length) and the vertical axis is V, the volume that your box has for a given s. You should see that, as s increases from 0, so does the volume...up to a certain point...then the volume equation comes down again even though the side length is still increasing.

6. anonymous

You have to find the maximum point with your calculator.

7. anonymous

You should find that the maximum volume occurs for s=2.5.

8. anonymous

Okay?

I am trying to follow the Volume.jpg. where you transition from:$V=(s ^{2}(A-s ^{2}))/4s$ to$As/4-s ^{2}/4$ I am coming up with $As/4-s ^{3}/4$ Where am I going wrong?

10. anonymous

$A=4 \times (side.area)+(area.of.base)= 4sh+s^2$so$h=\frac{A-s^2}{4s}$Since$V=s^2h \rightarrow V=s^2.\frac{A-s^2}{4s}=\frac{s}{4}(A-s^2)$

11. anonymous

You weren't going wrong.

O.K Just looks different LOL

13. anonymous

I dropped a superscript on paper.

14. anonymous

No, there's an error in what I derived.

I like the use of attachments

16. anonymous

When they're correct... :(

Thanks for clearing things up for me. When you are treading on new ground, sometimes you lose your confidence. I was unsure, thanks again.

18. anonymous

Dscribblez, ignore the scans...the equations typed above are correct. You need to plug the one for V into your calculator and estimate the s that gives you the greatest positive value of V.

19. anonymous

20. anonymous

21. anonymous

The maximum value occurs at the intersection of the line and the cubic. The exact s-value is$s=\sqrt{\frac{5}{3}}$but I'm thinking if you quote that, your teacher might think you've cheated. Plot it, estimate it. Good luck.