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TASK: Investigation with square sheets: From a square sheet of paper 20 cm by 20 cm, we can make a box without a lid. We do this by cutting a square from each corner and folding up the flaps.
Q-1-Find a relationship (general rule) between the size of paper(y) and the size of cut(x) that produces the maximum volume?
Q- 2-Test the validity of your general rule by using different values of a, b, and Justify your answer and its degree of accuracy.
Q- 3-Discuss the scope or limitations of the general statement.
Q- 4-Draw a graph Volume (V) and side of square (x) with the suitable scales.
Four questions ,it is not possible to answer in this form ,maxumum 1 question you can ask .
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Let we have sheet of paper of size `yxxy` , we wish to prepare a box ,buy cutting square from each corner of size `x xx x` .Each side of
square reduced to length = y-2x , It is clearl to understand `y-2x>0` .
Thus volume of soformed box will be
`V=(y-2x)^2 xx x`
For maximum volume with fixed m ,we need to find derivative ,and solve the problem.
for max/min `(dV)/(dx)=0` ,
`y-2x!=0` ,otherwise box is not possible.
S0 x=y/6 ,will give maximum volume of the box.
For validity please substitute the values of y and x separately your self.
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