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TASK: Investigation with square sheets: From a square sheet of paper 20 cm by 20 cm, we...

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user3496714 | (Level 2) eNoter

Posted March 26, 2013 at 2:08 PM via web

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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 .

pls pls pls pls pls pls pls for godsake pls do this questions if u can then pls in this q.1,2,3 are very important so pls do them together. i cannot post it again so pls pls sir

1 Answer | Add Yours

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 27, 2013 at 6:42 AM (Answer #1)

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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` ,




`x=y/6`  ,

`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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