Open box problem
The Open Box Problem Aim: To determine the size of the square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. Part 1 I will be investigating the size of the cut out square which makes an open box of the largest volume for any sized square sheet of card. The volume for any sized square sheet of card will be gained by using the following formula. Volume = height × area of base V = x × ((L - 2x) × (W - 2x)) X = height of cut out square L= length of square W = width of square I am going to use the following formula to work out the volume of an 8cm by 8cm square sheet of card. I am going to keep the size of card the same while changing the height of the cut out square. V = x × ((8 - 2x) × (8 - 2x)) SQUARE Length (L)cm Width (W)cm Height (X)cm Volume cm3 (2dp) 8 8 0 0.00000 8 8 0.25 4.06250 8 8 0.5 24.50000 8 8 0.75 31.68750 8 8 36.00000 8 8 .25 37.81250 8 8 .5 37.50000 8 8 .75 35.43750 8 8 2 32.00000 8 8 2.25 27.56250 8 8 2.5 22.50000 8 8 2.75 7.18750 8 8 3 2.00000 8 8 3.25 7.31250 8 8 3.5 3.50000 8 8 3.75 0.93750 8 8 4 0.00000 From the table above it can clearly be seen that the biggest volume gained from an 8 by 8 piece of square sheet is 37.81cm (2dp), this volume lies between the height of 1cm and 1.5cm. Therefore I am going to further
Personal Exercise Program
GCSE PE COURSEWORK Task: Plan a training programme for a specific activity. I have decided that I am going to use football as the activity that my training programme is going to be based on. I will perform my circuit in the gym. My general health is very good. I do not suffer from asthma or any other breathing problems and I have no allergies. I eat quite healthily getting lots of carbohydrates especially as well as proteins, starch, vitamins and all the required fats. Firstly I am going to show how much exercise I would do in a typical week. * 3 hours of in school games lessons * Half an hour of football training for school * 45 minutes of cricket training for school * 1 hour of football training for Bishops Lydeard YFC * 1 hour and 20 minutes matches on Sundays Bishops Lydeard YFC. * 1 hour cricket training for Fitzhead CC * 3-4 hours of football at lunch break for leisure As you can see I am already a very active person which helps me towards being a very fit person. Stamina is my main strength which is why I normally compete in long distance events on sports days and I am good at the bleep test. It is for all these reasons that I will be trying to push myself to my limit. The two areas of specific fitness I will be working on to make my performance levels in football higher are AGILITY and UPPER BODY STRENGTH. Agility is a major component of football. Being
