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.

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Presentation transcript:

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

1 cm 18 cm 1 cm 1 cm 18 cm 1 cm

18 cm 1 cm

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

20 cm

2 cm 16cm 2 cm 2 cm 16cm 2 cm

2 cm 16cm 2 cm

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

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

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?