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- 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.
Q- Draw a graph Volume (V) and side of square (x) with the suitable scales.
we have sheet 20 x 20 .let square of side x cut from each corner.Let it folded and form a box.
let V be the volume of the box. Then 2x length reduced from each side.
`V=(20-2x)^2xxx` , for getting max V ,we use calculus and calculate derivative
For max dv/dx=0 , (20-2x)(20-6x)=0
x=10 ,not possible then there will no box
max v=(20-20/3)^2(10/3)=16000/27 cubuc cm.