1. 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. Will you get the same volume irrespective of the size of the squares that are cut out? Investigate what volumes are possible for different sizes of cut-out squares. What is the maximum possible volume and what size cut produces it?
20 cm

2. 1 cm
18 cm
1 cm
1 cm
18 cm
1 cm

3. 18 cm
1 cm

4. Vol = L x B x H
18 cm
= 18 x 18 x 1
1 cm
= 324
18 cm

5. 20 cm

6. 2 cm
16cm
2 cm
2 cm
16cm
2 cm

7. 2 cm
16cm
2 cm

8. 16cm
Vol = L x B x H
2 cm
= 16x 16x 2
= 512
16cm

9. Length of side of square cut out
Length of Cuboid
Breadth of cuboid
Height of cuboid
Volume of cuboid 1 18
324 2 16 …

10. Continue the Investigation. Find the box with maximum volume.
What is the maximum possible volume and what size cut produces it?
What can we do graphically to represent the results?
How does this relate to differentiation?