SOLUTION: a pan is to be formed by cutting 2cm by 2cm squares from each corner of a square piece of sheet metal and then folding the sides.if the volume of the pan is to be 441cm squared,wha

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Question 948045: a pan is to be formed by cutting 2cm by 2cm squares from each corner of a square piece of sheet metal and then folding the sides.if the volume of the pan is to be 441cm squared,what are the dimensions of the original piece of metal sheet?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ASSING VARIABLES
h=2, the sidelength of square to cut and remove
x, the dimensions of the initial square piece to form the pan
v=441, volume of resulting open pan

%28x-2h%29%28x-2h%29h=v which is a quadratic equaion in the unknonw variable, x.
x%5E2-4hx%2B4h%5E2=v%2Fh
x%5E2-4hx%2B4h%5E2-v%2Fh=0
-
Or better, take advantage of the square part of the expressions,
%28x-2h%29%5E2=v%2Fh
x-2h=0%2B-+sqrt%28v%2Fh%29
highlight%28x=2h%2B-+sqrt%28v%2Fh%29%29, completely in symbolic form; and understand that one of these
solutions will be good and the other will be meaningless.

Substitute the values:
x=2%2A2%2B-+sqrt%28441%2F2%29
You want the PLUS square root form.
highlight%28x=4%2B21%2Fsqrt%282%29%29


You might want to show this as highlight%28%288%2B21%2Asqrt%282%29%29%2F2%29.
About 18.849 or 18.9.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a pan is to be formed by cutting 2cm by 2cm squares from each corner of a square piece of sheet metal and then folding the sides.
if the volume of the pan is to be 441cm cubed,
what are the dimensions of the original piece of metal sheet?
:
cutting 2cm squares from the corners will make the dimensions of the pan 4cm less than the dimensions of the original sheet metal, the height will be 2 cm
:
Let s = the length of the side original sheet metal square
therefore
2(s-4)*(s-4) = 441
Foil
2(s^2 - 4s - 4s + 16) = 441
2(s^2 - 8s + 16) = 441
2s^2 - 16s + 32 - 441 = 0
2s^2 - 16s - 409 = 0
Use the quadratic formula to find s; a=2; b=-16; c=-409
I got a positive solution of
s = 18.85 cm is the side of the original square piece of metal
: