SOLUTION: PLEASE HELP ME!!!! Here's the question: An open box is formed from a square of cardboard by cutting a 3cm sqaure from each corner and folding up the edges to form sides. If the vo

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Question 15791: PLEASE HELP ME!!!! Here's the question:
An open box is formed from a square of cardboard by cutting a 3cm sqaure from each corner and folding up the edges to form sides. If the volume of the box is 60cm^3, find the dimensions of the box,
Thanks in advance
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the side of the original square of cardboard be x cm.
If you now cut out 3 cm squares from each corner, the remaining side of the cardboard square is now (x - 2*3) = (x - 6) cm and this is the size of one side the bottom of the finished box.
The dimensions of the finished box is then, (x - 6)cm by (x - 6)cm by 3cm high.
The volume of the finished box is given as 60 cm^3. So now we can set up the equation to solve for x, the length of the side of the original square from which the box is made. We'll use the formula for the volume of a rectangular prism (AKA box): V = Bh where B is the area of the base and h is the height of the box.
%28x+-+6%29%28x+-+6%29%283%29+=+60 Expand the left side.
%28x%5E2+-+12x+%2B+36%29%283%29+=+60 Divide both sides by 3.
x%5E2+-+12x+%2B+36+=+20 Subtract 20 from both sides.
x%5E2+-+12x+%2B+16+=+0 Solve this quadratic equation using the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a
x+=+%28-%28-12%29%2B-sqrt%28%28-12%29%5E2+-+4%281%29%2816%29%29%29%2F2%281%29
x+=+%2812%2B-sqrt%28144+-+64%29%29%2F2
x+=+%2812%2B-sqrt%2880%29%29%2F2
x+=+6+%2B+2sqrt%285%29 or x+=+6+-+2sqrt%285%29
Let's look at the first root: x+=+6+%2B+2sqrt%285%29 = 6+%2B+2%282.24%29 = 10.47
Now the second root: x+=+6+-+2sqrt%285%29 = 6+-+2%282.24%29 = 1.53
Clearly, the second root can be discarded because if that were the length of the side of the original square, then you could never have cut two 3-cm corners from it.
The first root: x = 10.47cm (Approx) is the length of the side of the original square.
Check:
%2810.47+-+6%29%5E2+%2A+3+=+59.9427+ This is not quite 60 because when we took the square root of 5, we got an approximate value.