Question: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.
Answers:
Drawing a picture of this problem helps. Anyway, set up the equation 100= V. V=LxWxH. 100= 2*X*2X . You get the 2 from the corners, X is one side. 2X is the other side.
100=4X^2
25=X^2
5=X
5+2+2= 9 =side 1
5*2 = 10 + 2 + 2 = 14 = side 2
so original sheet was 9 x 14 inches
2*2x*x=100
Solve for x.
4x^2=100
x^2=25
x=5
so 10"x5"x2" is the box dimensions
Add 4 (2 on each side) to the width and length for the sheet.
14"x9"
14" by 9"
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