An open box is to be made from a rectangular piece of tin by cutting 2-inch squares out of the corners and fol
An open box is to be made from a rectangular piece of tin by cutting 2-inch squares out of the corners and folding up the sides. The length of the finished box is to be twice the width. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
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9 inches by 14 inches.
volume = 100 = L x W x H
100 = L x W x 2 (since the side of the squares cut from the corners be the height of the box)
L x W = 50
since L = 2W (length is twice the width)
then
2W x W = 50 (substitute 2W in place of L)
or
2W² = 50
W² = 25 (divide both sides of the equation by 2)
taking the square root
W = 5
thus
L = 2W = 2(5) = 10
adding the sides of the the squares from the corners
length of the sheet = 2 + L + 2 = 2+10+2 = 14
width of the sheet = 2 +W + 2 = 2 + 5 + 2 = 9
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Let the length and width of the tin be l and w.
Let the length and width of the box be l’ and w’.
l’=2w’
Volume of the box=2l’w’=100 =>2(2w’)w’=4w’2^2=100
or w’=5
l’=2w’=10
l=l’+4=14
w=w’+4=9
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