Maths Coursework;
Trays
In this coursework candidates were given a task entitled "Trays." The task consisted of a shopkeeper's statement upon the volume of a tray which was to be made from an 18x18 piece of card. The shopkeeper's statement was that, "When the area of the base is the same as the area of the four sides, the volume of the tray will be maximum." By saying this, the shopkeeper basically meant that when the area of the base of the tray is equal to the total area of the sides the volume of the tray will be at its highest. We were told to investigate this claim.
Plan.
. I will investigate the different sizes of tray possible from an 18x18 piece of card.
2. After gaining my results I will then put them in a table.
3. I will try to spot any patterns from my table.
4. I will express any patterns or other formulae in mathematical notation.
To investigate the different volumes given by different trays, I first decide to cut the corners in ascending order from 1-8. (The longest possible corner could only be 8 as after this there would be no base.) After this I worked out the formula needed to work out the volume for the various trays. For the corner size 1x1 the way I worked out the volume was 16x16x1 which equalled 256cm. Thus the formula to work out the volume for a tray made by an 18x18cm card is (n - 2X) x X. In this formula the letter "X" represents the size of the corner. I tried my formula for the corner length of 2cm,
Trays
In this coursework candidates were given a task entitled "Trays." The task consisted of a shopkeeper's statement upon the volume of a tray which was to be made from an 18x18 piece of card. The shopkeeper's statement was that, "When the area of the base is the same as the area of the four sides, the volume of the tray will be maximum." By saying this, the shopkeeper basically meant that when the area of the base of the tray is equal to the total area of the sides the volume of the tray will be at its highest. We were told to investigate this claim.
Plan.
. I will investigate the different sizes of tray possible from an 18x18 piece of card.
2. After gaining my results I will then put them in a table.
3. I will try to spot any patterns from my table.
4. I will express any patterns or other formulae in mathematical notation.
To investigate the different volumes given by different trays, I first decide to cut the corners in ascending order from 1-8. (The longest possible corner could only be 8 as after this there would be no base.) After this I worked out the formula needed to work out the volume for the various trays. For the corner size 1x1 the way I worked out the volume was 16x16x1 which equalled 256cm. Thus the formula to work out the volume for a tray made by an 18x18cm card is (n - 2X) x X. In this formula the letter "X" represents the size of the corner. I tried my formula for the corner length of 2cm,
