Square Volume

[Tinker21]

Use an 8”x10” sheet of paper (cut an 8.5”x11” to size if you need to) to create a rectangular box without a top. To do this, you cut equal sized squares out of each corner and fold up the sides. Tape the corners together and you have a box.

(a) What is the volume of your box with 1” by 1” squares cut out of each corner? How does the volume change with different size squares, say 2” by 2” and 1.5” by 1.5”.

(b) Now let’s theorize, if you ‘cut’ out an x” by x” square from each corner, what is the formula for the volume of your box in terms of x (Volume=?)?

(c) What values of x are possible (maximum reasonable) in part (b)?


I cannot even begin to figure out how to answer this question. I cannot even figure out what formula to use to answer this question. Can someone please help me totally confused. :?

 

[Deleted member 4993]

Use an 8”x10” sheet of paper (cut an 8.5”x11” to size if you need to) to create a rectangular box without a top. To do this, you cut equal sized squares out of each corner and fold up the sides. Tape the corners together and you have a box.

(a) What is the volume of your box with 1” by 1” squares cut out of each corner? How does the volume change with different size squares, say 2” by 2” and 1.5” by 1.5”.

(b) Now let’s theorize, if you ‘cut’ out an x” by x” square from each corner, what is the formula for the volume of your box in terms of x (Volume=?)?

(c) What values of x are possible (maximum reasonable) in part (b)?


I cannot even begin to figure out how to answer this question. I cannot even figure out what formula to use to answer this question. Can someone please help me totally confused. :?

First draw a sketch of the problem.

If you cutof square of side 'x' from corners, the bottom of the box will have length of (10-2x)" and width of (8-2x)" and the depth of the box is "x".

What is the volume of this box?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[albie09]

...and the sides of the cutout needs to be less than 4 or the width of the construction goes away.