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 cutout squares ID: 673297
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Slide1
20 cm
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?Slide2
1 cm
1 cm
18 cm
1 cm
18 cm
1 cmSlide3
1 cm
18 cmSlide4
1 cm
18 cm
18 cm
Vol
= L x B x H
= 18 x 18 x 1
= 324Slide5
20 cm Slide6
2 cm
2 cm
16cm
2 cm
2 cm
16cmSlide7
2 cm
2 cm
16cmSlide8
2 cm
16cm
Vol
= L x B x H
= 16x
16x
2
= 512
16cmSlide9
Length of side of square cut out
Length of Cuboid
Breadth of cuboid
Height of cuboid
Volume of cuboid11818
13242
16………
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Square with length 1 cm
Vol
= 324Slide11
Square with length 2 cm
Vol
= 512Slide12
Square with length 3cm
Vol
= 588Slide13
Square with length 4cm
Vol
= 576
Volume is starting to decrease again so the maximum volume is between 3 and 4Slide14
Max
Vol
= 592.59
Length of square for Max
Vol
= 3.33 cmSlide15
x
x
Vol
=L x B x H
20 - 2x
20 - 2x
= (20-2x)
X (20 - 2x)
X (x)
Vol
=(20-2x)(20-2x)(x) Slide16
Volume
When
the volume is 0
So
and the volume is
Differentiate
Find stationary points