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.
let square of side 1cm cuts
let side of square be 2cm
let n is side of square,where n is less or equals to 9, n is natural no.
this is the relation between side of square and volume
v=(20-2n)^2.n n is natural