SOLUTION: please help me with this problem, Thanks! A box without a top is to be constructed from a square metal sheet by cutting 3 square centimeters from each corner of the sheet and

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Question 14771: please help me with this problem, Thanks!
A box without a top is to be constructed from a square metal sheet by cutting 3 square centimeters from each corner of the sheet and
bending up the sides. Find the size of the original square if the volume of
the constructed box is to be 867 cubic centimeters.
(Hint: the volume is given by V = L.W.H)
Thanks again!!
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Let the length of the side of the bottom of the box = x cm.
The height of the box is 3 cm.
Using the formula for the volume:
Divide both sides by 3
Take the square root of both sides.
x = +/-17 cm. You can discard the negative root and use only the positive root since length can't be a negative quantity.
Answer: 17 cm. This is the length of the side of the bottom of the box. Now add the 2 corners that were cut out to make the sides of the box (2 X 3 cm) to get the length of the sides of the original square.
17 + 2(3) = 23 cm.
Check:
V = 3(17)^2 = 3(289) = 867
There is one additional step needed to answer the question: "What is the size of the original square?"
The 17 cm found above is the length of the side of the original square minus the the 3-cm corners cut out. Since we cut out two corners on each side, we have to add 2(3 cm) to the 17 cm to get 23 cm for the side of the original square.