# 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-...

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- Investigate what volumes are possible for different sizes of cut-out squares.

Q- Suggest a relationship between Volume (V) and side of square (x).

Q- Draw a graph Volume (V) and side of square (x) with the suitable scales.

Q- What is the maximum possible volume and what size cut produces it?

Q- Try same with different sized(10 cm, 30 cm, 40 cm, 50 cm, 100 cm ) square sheets of paper.

Q-Find a relationship (general rule) between the size of paper(y) and the size of cut(x) that produces the maximum volume?

Q- Test the validity of your general rule by using different values of a, b, and Justify your answer and its degree of accuracy.

Q- Discuss the scope or limitations of the general statement.

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### 1 Answer

20.20

let square of side 1cm cuts

v=18.18.1

let side of square be 2cm

v=16.16.2x

let n is side of square,where n is less or equals to 9, n is natural no.

v=2.2.n

this is the relation between side of square and volume

v=(20-2n)^2.n n is natural