Question 1207436: Every time I come across this question it throws me into a loop.
The part about removing a foot from each corner is the confusing part to me.
An open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges.If the box is to hold 4 cubic feet,what should be the dimensions of the sheet metal?
Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Make a drawing according to the description and label the parts. Form your necessary equation based on that.
A shaped piece square will be removed at each corner of the original piece of sheet metal.
Say the length of the sheet metal square before taking off the corners is x.
Then the AREA of the sheet is x^2. Unit is square feet.
Next is cut off 1 foot by 1 foot at each corner;
.
.
----the rest of solution removed ----
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
x = side length, in feet, of the original square sheet metal
x > 0
The square of side length x is reduced to side length x-2 when subtracting 1 foot from each side.
Notice I subtracted two copies of "1 foot" from each dimension.
volume = length*width*height
volume = (x-2)*(x-2)*1
volume = x^2 - 4x + 4
Set this equal to the volume we want to get,
x^2 - 4x + 4 = 4
x^2 - 4x = 0
x(x-4) = 0
x = 0 or x-4 = 0
x = 0 or x = 4
Ignore x = 0 since it doesn't make x > 0 true.
The only possible answer is x = 4.
The original square sheet metal is 4 by 4.
Subtract off 1 ft for each side to get a 2 by 2 square floor of the box when folding up the sides. Each flap is 1 ft tall.
volume = length*width*height = 2*2*1 = 4 cubic feet
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
An open box is to be constructed from a square piece of sheet metal
by removing a square of side 1 foot from each corner and turning up the edges.
If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?
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M E N T A L S O L U T I O N
The height of the open box should be 1 foot.
Hence the area of the base of the box must be 4 ft^3 : 1 ft = 4 ft^2.
The base is the square (OBVIOUSLY) and its area is 4 ft^2.
Hence, the side of the base square is 2 feet.
It means that the original sheet of the metal is the square with the side length
1 + 2 + 1 = 4 ft ANSWER
Solved.
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It is a JOKE ENTERTAINMENT Math problem for MENTAL SOLUTION.
To see many other similar solved problems with full explanations, look into the lesson
- Making a box from a piece of cardboard
in this site.
Read, enjoy, and learn the whole subject from there.
Have fun ( ! )
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The solution in the post by @josgarithetic is TOTALLY WRONG,
so you better IGNORE it, for safety of your mind.
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