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# help

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A closed rectangular box has a surface area of 1000 square cm. The length of the box is twice its width and the height is six times its width. What is the volume of the box?

May 12, 2020

#1
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So the surface area of a rectangular prism is 2wh + 2wl + 2hl

l = 2w

h = 6w

w = w

So replacing all terms with w, we have

2w * 6w + 2w * 2w + 2 * 2w* 6w = 12w^2 + 4w^2 + 24 w^2 = 40w^2 = 1000

w ^ 2 = 1000/40 = 25

w = sqrt(25) = 5

l = 2*5 = 10

h = 6*5 = 30

10*30*5 = the volume = 1500 cm^3

If you don't understand anything feel free to ask.

May 12, 2020
#2
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L = 2W

H = 6W

Surface area  =   2 (WL + HL + HW)....so we  have

1000 =  2 [ ( W (2W)  + (2W)(6W)  + W(6W) ]       simplify

1000  =  2  [ 2W^2  + 12W^2  + 6W^2 ]

1000  =  2 [ 20W^2]

1000  = 40W^2         divide both sides  by  40

1000 /40 =  W^2

100/4  =   W^2

25  =  W^2      take the positive  root

5  =  W

So.....L = 2W   =  10

And  H  =  6W =  30

So...the  volume  =  W * L * H  = ( 5) ( 10)  ( 30) =   1500 cm^3   May 12, 2020