## anonymous one year ago 2700 of material is avaiblr to make a boc with a square base and a open top. determine the largesst volume of the box

1. anonymous

@ganeshie8

2. anonymous

the open top thing is confusing me

3. anonymous

i am only missing 2700 cm2

4. ganeshie8

|dw:1433741377518:dw|

5. ganeshie8

surface area of box = (surface area of base) + (surface area of sides) = x^2 + 4xh we're given surface area equals 2700, so $x^2+4xh=2700\tag{1}$

6. ganeshie8

next, see if you can write an expression for the volume of box

7. anonymous

o yea i think the SA formula was confusing me how do u get it

8. anonymous

@ganeshie8 is the vloume=lwh

9. ganeshie8

for surface area, you just add up the areas of all the sides

10. ganeshie8

how many sides does that box have ?

11. anonymous

um 6

12. ganeshie8

careful, it has no top

13. ganeshie8

there is one base, which is a square and four lateral sides

14. ganeshie8

so in total it has 5 faces

15. ganeshie8

whats the area of base ?

16. anonymous

x2?

17. ganeshie8

Yes, area of base = $$x^2$$

18. ganeshie8

next notice that each lateral face has same dimensions : width = x height = h

19. ganeshie8

|dw:1433742821286:dw|

20. ganeshie8

what is the area of that lateral face ?

21. anonymous

um h * w

22. ganeshie8

w = x here right

23. anonymous

yes

24. ganeshie8

since the box has four lateral faces, the lateral area is simply $$4*xh$$

25. ganeshie8

so do you get how i arrived at the surface area equation $$(1)$$

26. anonymous

oh ok yea

27. ganeshie8

the expression for volume would be $V = x*x*h = x^2h\tag{2}$

28. ganeshie8

solve $$h$$ from first equation and plug it in abvoe

29. anonymous

so what does the open top do ?

30. ganeshie8

it does nothing, do you have "h" from first equation ?

31. ganeshie8

from first equation, $x^2+4xh=2700\\~\\\implies 4xh=2700-x^2\\~\\\implies h = \frac{675}{x}-\frac{x}{4}$ yes ?

32. anonymous

h=V/x2

33. anonymous

okey yea i tryed it and my final answer is 135000 , what u get ?

34. ganeshie8

do you mean 13500 ? http://www.wolframalpha.com/input/?i=maximize+x*%282700-x%5E2%29%2F4%2Cx%3E0

35. anonymous

oh sorry yea

36. anonymous

so the open top is just for confusing ?

37. anonymous

i should ignore it the next time i see it ?

38. ganeshie8

what do you mean you should ignore it

39. ganeshie8

the surface area changes if it was not open top

40. anonymous

how would it look like then ?

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