Painting The Gym Assignment
By: Emma Chickles 7F
The assignment is to find the cost if the Canadian International School of Hong Kong were to repaint the lines and varnish the entire gymnasium floor. This project links with the AOI of Community and Service because doing this service, it will prove me as a responsible citizen; a essential concept of Community and Service. This also links with Human Ingenuity because we are required to use our prior knowledge to create and investigate into the measurements of the gym. My estimation for thickness of all the lines would be the same, at 3 centimeters. My estimation for the area of all the lines in the main basketball court is 10 meters squared. My estimation for the area of all the lines in a smaller basketball court is 6 meters squared. My estimation for the area of all the lines in one volleyball court is 5 meters squared. My estimation for the area of all the lines in one badminton court is 2 meters squared. My estimation for the entire gym is 300 meters squared. My estimation for the total cost of paint would be around $1000 HKD.
I found the area of the semi-circular line by finding the radius of the it. I could have gotten a bendable measuring tape, but that could be inaccurate because the measuring tape could be bent oddly, making the result incorrect. The way I measured had a down side as well, as it is only a semi-circle, using the Trundle Wheel, we couldn’t be sure if I was measuring in a straight line, however there was less risk of the result of being inaccurate this way than measuring with the measuring tape, since measuring tapes aren’t meant to be bent.
Here is my sketch of the entire gym.
Key:
Red Lines ~ Main Basketball Court
Black Lines ~ Smaller Basketball Courts
Blue Lines ~ Volleyball Courts
and
White Lines ~ Badminton Courts
*I made a mistake in the Volleyball courts, the middle volleyball court is supposed to be on its side*
I was able to find the perimeter of a court by using the formula 2 length plus 2 width. For example, I found perimeter of the badminton court by first measuring the length of the line and the width of the line. The length is 14.48 and the width is 6.16. This is the best way because the formula of 2 length plus 2 width, will always give the perimeter. Another way to find the area is to use the Trundle Wheel, and wheel it all the way around the court. This is not the best way because there is more risk of mistake since the Trundle Wheel would have to turn at the corners, therefore, it may not give a accurate result. Where as, the way I’ve done, you only have to measure 2 separate, straight lines. Therefore it is the best way.
Besides the measurements of the lines, I also need to find the area of all the lines, if I find out that, I can find out how much paint will be used and the cost. To find the area, you have to multiply the width by the length. To clearly show all the findings I have found, I put it in a pacific format, consistent within a document. For example, for the Volleyball Court, the following was what I recorded “Volleyball Courts (3) - Blue Lines:
Length: 18.03m
Width: 9.03m
Perimeter: 54.12m
(18.03 x 2) + (9.03 x 4) = 72.18
Line Width: 5cm or 0.05m
1 Court, Area of the Lines: 3.609m squared
3 Courts: 10.827m squared”.
Computer technology has also helped me in this project as the Calculator has helped me ensure my calculations are correct.
The measurements I made for the main basketball court are, for the length is 18.36m, the width 14.33m, the key 14.36m, the semi-circle in the key is 5.20m, the semi-circle outside the key is 8.57m, the three-point line is 24.10m, the line width for the three-point line is 0.054m and for the other lines, the line width is 0.041m.
The measurements I made for the smaller basketball court, the perimeter is 74.85m, the key is 11.32m, the semi-circle in the key is 4.80, the semi-circle outside the key is 5.20m, the three-point line is 15.30m, and the width of al the lines is 0.042m.
The measurements I made for the volleyball court, for the length is 18.03m, the width is 9.03m and the width of the lines is 0.05m.
And lastly, the measurements I made for the badminton court are, for the length is 14.48m, the width is 6.16m and the line width is 0.039m.
After finding the measurements, I had to find the area of the line. To do this, I multiplied the total length of all the lines and multiplied it by the line width. For example, when calculating the total area of the lines for one volleyball court I took into account that there is 4 lines that have the width measurement; 9.08m, and 2 lines that have the length measurement; 18.03m, as shown below. As I added them all together using this operation, (18.03 x 2) + (9.03 x 4), I got 72.18m. The line width is 5cm, or 0.05m, was then multiplied by the total length of the lines; 72.18, resulting as 3.609m squared. There are 3 volley ball courts so I multiplied 3.609 by 3, 10.827m squared; the total area of all the lines! After finding the area of all the lines, from all the courts, I got 53.39464m squared. Since I know that 1L of paint covers 20m squared, I divided 53.39464m squared by 20m squared, then multiplied that by 120, since 1L costs $120.00 HKD.
When preparing to measure the lines, I noticed that the Trundle Wheel I had borrowed was broken, and would be useless when attempting to measure the lines. This problem was overcome by sharing a Trundle Wheel another group who was also measuring that day. Although this problem made me contribute less, I did as much as I can and I believe I was exceptionally useful when recording the data neatly. I could have also solved this by using meter sticks or measuring tapes, but Trundle Wheels really is the most effective measuring instrument in this situation. When I was at the gym, I also realized we needed a ruler to effectively measure the width of lines. One of our group members went back up to the classrooms to get one. Because of this, I have to regret not being prepared with the needed measuring instruments. Another problem I had was when I was calculating the area of the lines. Thankfully, I realized my mistake when sketching the entire gym including all the courts, I had only added the lines for one court, meaning I only calculated the area of the lines for 1 badminton court instead of 7 courts. So I had to go back to my measurements and make more calculations on that and the total area of the lines of all the court, as well as the total cost of paint and the total cost of everything. I decided to do it this way, the longer way, because I can be sure that it is accurate, as I could lose track of what I’ve added. And lastly, when at the beginning of calculating, the process was relatively slow, as I did it with pen and paper. I fixed this by using a calculator on my computer, recommended by a friend.
I believe the total area of the gymnasium is 484.459m squared, meaning the total cost of varnish would be $4844.59001 HKD. I believe the total area of all the lines is 53.39464m squared, meaning the total cost of paint $320.36784 HKD. Resulting in that the total cost of both the varnish and paint is $5164.95785 HKD. I believe my answer is accurate since around three quarters of the time I used a calculator to calculate, instead of using scrap paper, and the calculations on the scrap paper was double checked by the calculator. However, it may not be accurate since many people had different final answers as me, but after checking, and re-checking my calculations I can’t find where I got it wrong, unless the measurements were incorrect. If I could do this assignment again, I would like to measure the gym myself, only myself. I would prefer to have the measuring be slow, to make sure that it is accurate.
