TRAYS
Firstly I am going to investigate the shopkeeper's statement.
If the width of the side of the tray is represented by the letter w then we have:
So The volume of the tray = w (18cm - 2w)(18cm -2w)
Results Table
Width of Side (cm)
Length of base (cm)
Volume (cm3)
Area of Side (cm2)
Area of all sides(cm2)
Area of base (cm2)
6
256
6
64
256
2
4
392
28
12
96
3
2
432
36
44
44
4
0
400
40
60
00
5
8
320
40
60
64
6
6
216
36
44
36
7
4
12
28
12
6
8
2
32
6
64
4
Conclusion
The results table and the diagrams above prove that the shopkeeper's statement is true as you can see by the blue highlighted part of the results table above.
Now I have discovered that the shopkeeper's statement is true I will investigate this further by finding out if the statement is true for other sized squares.
24cm x 24cm square
The first square I will investigate is a 24cm x 24cm square. My prediction is that the shopkeeper's statement will also be true for a square of this size.
If the width of the sides is represented by W then we have:
So the volume of the tray = w(24cm - 2w)(24cm - 2w)
Results Table
Width of Side (cm)
Length of base (cm)
Volume (cm3)
Area of Side (cm2)
Area of all sides(cm2)
Area of base (cm2)
22
484
22
88
484
2
20
800
40
60
400
3
8
972
54
216
324
4
6
024
64
256
256
5
4
980
70
280
96
6
2
864
72
288
44
7
0
700
70
280
00
8
8
512
64
256
64
9
6
324
54
216
Firstly I am going to investigate the shopkeeper's statement.
If the width of the side of the tray is represented by the letter w then we have:
So The volume of the tray = w (18cm - 2w)(18cm -2w)
Results Table
Width of Side (cm)
Length of base (cm)
Volume (cm3)
Area of Side (cm2)
Area of all sides(cm2)
Area of base (cm2)
6
256
6
64
256
2
4
392
28
12
96
3
2
432
36
44
44
4
0
400
40
60
00
5
8
320
40
60
64
6
6
216
36
44
36
7
4
12
28
12
6
8
2
32
6
64
4
Conclusion
The results table and the diagrams above prove that the shopkeeper's statement is true as you can see by the blue highlighted part of the results table above.
Now I have discovered that the shopkeeper's statement is true I will investigate this further by finding out if the statement is true for other sized squares.
24cm x 24cm square
The first square I will investigate is a 24cm x 24cm square. My prediction is that the shopkeeper's statement will also be true for a square of this size.
If the width of the sides is represented by W then we have:
So the volume of the tray = w(24cm - 2w)(24cm - 2w)
Results Table
Width of Side (cm)
Length of base (cm)
Volume (cm3)
Area of Side (cm2)
Area of all sides(cm2)
Area of base (cm2)
22
484
22
88
484
2
20
800
40
60
400
3
8
972
54
216
324
4
6
024
64
256
256
5
4
980
70
280
96
6
2
864
72
288
44
7
0
700
70
280
00
8
8
512
64
256
64
9
6
324
54
216