basketball court investigation

By Emma Kious

Basketball court investigation

My taskMy 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 planThe steps I will go through to finish this task:Measure the area of each blue shapesMeasure the area of each red shapesMeasure the area of each white shapesFigure out how much paint will be needed for 1 basketball

court (2 coats)Figure out the costFind which team will provide cheaper servicesCalculate the total cost for 5 basketball courts (2 coats each)Present data and evidence to the logistics officer

MeasurementsHere are the diagrams with the measurements (the green does

not count as measured area)

Blue area

15 m

28 m

Area: 15x28 = 420 m2

420m2

Blue area

3.5 mArea: 3.5÷2 = 1.75 m1.75x1.75 = 3.06 m2

3.06x∏ = 9.6 m2

9.6 m2

Semi-circles

Red area

3.5 m 6 m

Area: 5.8x(3.5+6)5.8x9.5 = 55.1 m2

55.1m2

5.8 m

Red area

3.6 m

Area: 3.6÷2 = 1.8m1.8x1.8 = 3.24m2

3.24x∏ = 10.17m2

10.17m2

White area

5 cm15 m

28 m

Area: 2800x5 = 14000 cm2

1500x5 = 7500 cm2

14000x2 = 28000 cm2

7500x2 = 15000 cm2

28000+15000 = 43000 cm2

4.3m2

White area

5 cm

3.5 m6 m

5.8 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

White area

5 cm

Area: 3.6÷2 = 1.8 m1.8x1.8 = 3.24 m2

3.24x∏ = 10.17 m2

3.5÷2 =1.75 m1.75x1.75 = 3.06 m2

3.06x∏ = 9.6 m2

10.17-9.6 = 0.57m2

0.57m2

3.6 m 3.5 m

5 cm15 m

Area: 5x1500 = 7500 cm2

0.75m2

White area

5 cm3.5 m 3.4m

Area: 3.5÷2 = 1.75 m1.75x1.75 = 3.06 m2

3.06x∏ = 9.6 m2

3.4÷2 = 1.7 m1.7x1.7 = 2.89m2

2.89x∏ = 9.07 m2

9.6-9.07 = 0.53 m2

0.53x2 = 1.06 m2

1.06m2

1.6 m

1.5m

White area

5 cm 15 m

22.85m

Area:15÷2 = 7.5 m7.5x7.5 = 56.25 m2

56.25x∏ = 176.625 m2

1490÷2 = 745 cm745x745 = 555025 cm2

555025x∏ = 1742778.5 cm2

176.65-174.27 = 2.38 m2

2.38m2

4.3 + 1.7+ 0.57 + 0.75 + 1.06 + 2.38 = 10.76 m2

Total White area10.76 m2

55.1 + 10.17 = 65.27 m2

Total Red area65.27 m2

Total Blue area420 – 10.76 – 65.27 = 343.97 m2343.97

m2

Labor costsTeam 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)

3 painters = 15 ¥ per hour (per painter)1 supervisor = 45 ¥ per hour2 courts per 8 hours0.25 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 =

Labor costs : team 1

2 courts (2 coats)= 8 hours4 courts (2 coats) = 16 hours5 courts (2 coats)= 20 hours

1800 ¥

6 painters = 12.5 ¥ per hour (each painter)1 supervisor = 100 ¥ per hour4 courts per 8 hours0.5 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 =

Labor costs : team 2

4 courts (2 coats) = 8 hours5 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

Paint costs 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)

One litre of paint can cover 25 square metres

Blue area: 343.97m2

1 liter = 25 m2

1 can = 4 liters = 85 RMB 1 liter = 21.25 RMB

343.97 ÷ 25 = 13.75 liters13.75x2 = 27.5 liters27.5 ÷ 4 = 6.87 cans7 x 85 = 595 RMB

Blue paint (1 court)

2 coats

Red area: 65.27m2

1 liter = 25 m2

1 can = 2.5 liters = 95 RMB 1 liter = 38 RMB

65.27 ÷ 25 = 2.61 liters2.61x2 = 5.22 liters5.22 ÷ 2.5 = 2.08 cans3 x 95 = 285 RMB

Red paint (1 court)

2 coats

White area: 10.76m2

1 liter = 25 m2

1 can = 10 liters = 100 RMB 1 liter = 10 RMB

10.76 ÷ 25 = 0.43 liters0.43x2 = 0.86 liters0.86 ÷ 10 = 0.08 cans1x 100 = 100 RMB

White paint (1 court)

2 coats

Blue: 7x5 = 35 cans 545x5 = 2725 RMB

Red: 3x5 = 15 cans 285x5 = 1425 RMB

White: 1x5 = 5 cans 100x5 = 500 RMB

Total paint

Final paint Cost2725 + 1425 + 500 = 4650

4645 ¥

Total costTeam 2 + paint = 1750 + 4645 = 6395

6395 ¥

ReflectionMy 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.