By Emma Kious Basketball court investigation

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.

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

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

Blue area 15 m 28 m Area: 15x28 = 420 m 2 420m 2

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

Red area 3.5 m6 m Area: 5.8x(3.5+6) 5.8x9.5 = 55.1 m m m

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

5 cm 15 m 28 m Area: 2800x5 = cm x5 = 7500 cm x2 = cm x2 = cm = cm 2 4.3m 2

5 cm 3.5 m 6 m 5.8 m Area: 5.8x(3.5+6) 5.8x9.5 = 55.1 m x( ) m x9.3 = 53.4 m = 1.7 m 2 1.7m 2

5 cm Area: 3.6÷2 = 1.8 m 1.8x1.8 = 3.24 m x∏ = m 2 3.5÷2 =1.75 m 1.75x1.75 = 3.06 m x∏ = 9.6 m = 0.57m m m 3.5 m 5 cm 15 m Area: 5x1500 = 7500 cm m 2

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

5 cm 15 m 22.85m Area:15÷2 = 7.5 m 7.5x7.5 = m x∏ = m ÷2 = 745 cm 745x745 = cm x∏ = cm = 2.38 m m 2

= m 2

= m 2 Total Red area m 2

Total Blue area 420 – – = m m 2

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 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)

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) = 90 ¥ per hour (whole team) 8 hours = 90x8 = 720 ¥ 5 courts (2 coats)= 20 hours = 20x90 = Labor costs : team 1 2 courts (2 coats)= 8 hours 4 courts (2 coats) = 16 hours 5 courts (2 coats)= 20 hours 1800 ¥

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) = 175 ¥ per hour (whole team) 8 hours = 175x8 = 1400 ¥ 5 courts (2 coats)= 10 hours = 10x = 175 = Labor costs : team 2 4 courts (2 coats) = 8 hours 5 courts (2 coats) = 10 hours 1750 ¥

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

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

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

= ¥

Total cost Team 2 + paint = = ¥

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.