Algebra-Investigating Trays
Statement: The shopkeeper says, “When the area of the base is the same
as the area of the four sides, the volume of the tray will be a
maximum.”
Aim: To prove the shopkeeper’s statement true.
Task: To investigate this claim and investigate further.
18 x 18
I firstly started my trays investigation by drawing a net for a square
measured 18cm by 18cm. I then cut out this net square, after it had
been cut out I cut off 1cm off each of the four corners. This was so
the tray would join together.
I then calculated the area of the base. The formula I used to
calculate the area of the base was:
lxb For example:
Area of Base, tray 1
16x16=256cm
After this I then went on further to find the area of the four sides,
as I had used this square before. I then used the formula lx4 to find
the areas of the four sides, for example:
16x4=64cm
I then calculated the volume of the tray. The calculations I used to
find out the volume of the tray were:
14x14=256cm
= 256x2=512cm
The formula I used to calculate this was: lxbxh.
Height:
Base Length:
Volume:
Base Area:
Area of 4 sides:
1cm³
16cm³
256cm
256cm
1x16x4=64cm
2cm³
14cm³
392cm
196cm
2x14x4=112cm
3cm³
12cm³
432cm
144cm
3x12x4=144cm
4cm³
10cm³
400cm
100cm
4x10x4=160cm
5cm³
8cm²
320cm
64cm
5x8x4=160cm
6cm³
6cm
216cm
36cm
6x6x4=144cm