SOLUTION: Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square       Log On


   

Question 1114845: Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm^3.
Please help.
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
After folding, you get an open box.


Its base is the square with the side length of (x-2*4) = x-8 cm, where x is the side of the original cardboard.


The height of the box is 4 cm.


Hence,  4*(x-8)^2 = 144  is the volume equation.


It gives  (x-8)^2 = 144%2F4 = 36.


Hence,  x-8 = sqrt%2836%29 = 6.


Then x = 6+8 = 14.


Answer.  The side length of the original square piece of cardboard is 14 cm.

Solved.


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm^3.
----------------
Area of original square:: x^2
----
Area of base of box:: (x-8)^2
height of box:: 4 cm
--------
Equation:
4(x-8)^2 = 144 cm^3
-----
(x-8)^2 = 26
x-8 = sqrt(26)
x = 8+sqrt(26)
-----
Answer:: original dimensions are 8+sqrt(26) squared
-----------------
Cheers,
Stan H.
------------