Basketball court investigation

1. Basketball court investigation By Emma Kious

2. My task My task is to provide a quote of how much it will cost to paint 5 basketball courts. This quote will go to the head of logistics of a large sports complex and he will make a decision as to which quote will be used on completion of the task. The logistics officer will be considering the cost, quality of workmanship and would naturally expect that the quote is well organized and easy to read. He would be expecting to check your mathematical working to ensure that your costs have been formulated accurately. He has informed the school that he expects the job to be completed in less than 3 eight hour days.

3. Working plan The steps I will go through to finish this task: Measure the area of each blue shapes Measure the area of each red shapes Measure the area of each white shapes Figure out how much paint will be needed for 1 basketball court (2 coats) Figure out the cost Find which team will provide cheaper services Calculate the total cost for 5 basketball courts (2 coats each) Present data and evidence to the logistics officer

4. Measurements Here are the diagrams with the measurements (the green does not count as measured area)

6. Blue area 15 m Area: 15x28 = 420 m2 420m2 28 m

7. Blue area Semi-circles Area: 3.5÷2 = 1.75 m 1.75x1.75 = 3.06 m2 3.06x∏ = 9.6 m2 9.6 m2 3.5 m

8. Red area Area: 5.8x(3.5+6) 5.8x9.5 = 55.1 m2 55.1m2 3.5 m 6 m 5.8 m

9. Red area Area: 3.6÷2 = 1.8m 1.8x1.8 = 3.24m2 3.24x∏ = 10.17m2 10.17m2 3.6 m

10. White area Area: 2800x5 = 14000 cm2 1500x5 = 7500 cm2 14000x2 = 28000 cm2 7500x2 = 15000 cm2 28000+15000 = 43000 cm2 4.3m2 15 m 5 cm 28 m

11. White area 3.5 m 6 m Area: 5.8x(3.5+6) 5.8x9.5 = 55.1 m2 5.75x(3.4+5.9) m2 5.75x9.3 = 53.4 m2 55.1-53.4 = 1.7 m2 1.7m2 5 cm 5.8 m

12. White area 3.5 m 3.6 m 5 cm 15 m 5 cm Area: 3.6÷2 = 1.8 m 1.8x1.8 = 3.24 m2 3.24x∏ = 10.17 m2 3.5÷2 =1.75 m 1.75x1.75 = 3.06 m2 3.06x∏ = 9.6 m2 10.17-9.6 = 0.57m2 0.57m2 Area: 5x1500 = 7500 cm2 0.75m2

13. White area 1.5m Area: 3.5÷2 = 1.75 m 1.75x1.75 = 3.06 m2 3.06x∏ = 9.6 m2 3.4÷2 = 1.7 m 1.7x1.7 = 2.89m2 2.89x∏ = 9.07 m2 9.6-9.07 = 0.53 m2 0.53x2 = 1.06 m2 1.06m2 3.5 m 3.4m 5 cm 1.6 m

14. White area 22.85m 5 cm 15 m Area:15÷2 = 7.5 m 7.5x7.5 = 56.25 m2 56.25x∏ = 176.625 m2 1490÷2 = 745 cm 745x745 = 555025 cm2 555025x∏ = 1742778.5 cm2 176.65-174.27 = 2.38 m2 2.38m2

15. Total White area 4.3 + 1.7+ 0.57 + 0.75 + 1.06 + 2.38 = 10.76m2 • 10.76 m2

16. Total Red area 55.1 + 10.17 = 65.27m2 • 65.27 m2

17. Total Blue area 420 – 10.76 – 65.27 = 343.97m2 • 343.97 m2

18. Labor costs • Team One consists of 3 painters and one supervisor. The painters are paid 15RMB per hour and the supervisor will be paid at a rate of 45 RMB per hour. In 8 hours this set of painters can paint 2 courts ( both coats of paint.) • Team Two consists of 6 painters. These painters are paid 12.50 RMB per hour and a supervisor who is paid 100 RMB per hour. This group of painters can paint 4 courts in 8 hours. ( both coats of paint)

19. Labor costs : team 1 3 painters = 15 ¥ per hour (per painter) 1 supervisor = 45 ¥ per hour 2 courts per 8 hours 0.25 courts per hour 15x3 = 45 ¥ per hour (all painters) 45+45 = 90 ¥ per hour (whole team) 8 hours = 90x8 = 720 ¥ 5 courts (2 coats)= 20 hours = 20x90 = 2 courts (2 coats)= 8 hours 4 courts (2 coats) = 16 hours 5 courts (2 coats)= 20 hours 1800 ¥

20. Labor costs : team 2 6 painters = 12.5 ¥ per hour (each painter) 1 supervisor = 100 ¥ per hour 4 courts per 8 hours 0.5 courts per hour 12.5x6 = 75 ¥ per hour (all painters) 100+75 = 175 ¥ per hour (whole team) 8 hours = 175x8 = 1400 ¥ 5 courts (2 coats)= 10 hours = 10x = 175 = 4 courts (2 coats) = 8 hours 5 courts (2 coats) = 10 hours 1750 ¥

21. Labor costs The cheaper team is team 2 because they are faster, thus require less hours By hiring team two, you can save 50 ¥

22. Paintcosts • Blue paint costs 85 RMB for a 4 litre can (21.25 ¥ per liter) • Red paint costs 95 RMB for a 2.5 litre per can (38 ¥ per liter) • White paint costs 100 RMB per 10 litre can (10 ¥ per liter) Onelitreofpaintcancover25squaremetres

23. Blue paint (1 court) Blue area: 343.97m2 1 liter = 25 m2 1 can = 4 liters = 85 RMB 1 liter = 21.25 RMB 343.97 ÷ 25 = 13.75 liters 13.75x2 = 27.5 liters 27.5 ÷ 4 = 6.87 cans 7 x 85 = 595 RMB 2 coats

24. Red paint (1 court) Red area: 65.27m2 1 liter = 25 m2 1 can = 2.5 liters = 95 RMB 1 liter = 38 RMB 65.27 ÷ 25 = 2.61 liters 2.61x2 = 5.22 liters 5.22 ÷ 2.5 = 2.08 cans 3 x 95 = 285 RMB 2 coats

25. White paint (1 court) White area: 10.76m2 1 liter = 25 m2 1 can = 10 liters = 100 RMB 1 liter = 10 RMB 10.76 ÷ 25 = 0.43 liters 0.43x2 = 0.86 liters 0.86 ÷ 10 = 0.08 cans 1x 100 = 100 RMB 2 coats

26. Total paint • Blue: • 7x5 = 35 cans • 545x5 = 2725 RMB • Red: • 3x5 = 15 cans • 285x5 = 1425 RMB • White: • 1x5 = 5 cans • 100x5 = 500 RMB

27. Final paint Cost 2725 + 1425 + 500 = 4650 4645 ¥

28. Total cost Team 2 + paint = 1750 + 4645 = 6395 6395 ¥

29. Reflection My final quote appears to make sense because I know my formulas were correct (I think) and I did some pretty easy workings that made sense. I measured the court once using a measuring wheel and sometimes the measuring tape butt the measurements looked accurate. Even if I tried to be accurate, I didn’t really need to because in this case, having 1 or 2 liters of paint more isn't too much of a problem. Nevertheless, I think I should at least try to be accurate so it isn't completely off I chose to measure the court myself, not using the internet because I was never sure if the results on the internet were true, and If they were, if they were the same as our court. Some of my workings weren't correct, I might have multiplied by 2, or forgot to add a number but I think it is accurate enough for my results not to be too much out.