Ian See Tze Onn
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Mathematics
In this assignment we were asked to form a group and calculate the total surface area and volume of an irregular object. the object is given by the lecturer as it is shown on the left. There were many parts of the calculation and each of us were given a part to calculate. It was a tough shape to calculate as limited information was given. Nonetheless, my group managed to calculate the shape and hand the assignment on time.


For this section I used the law of cosine. To find the area of the segment i first have to find cos a using the formula: a²= b² + c² - 2(b)(c) cos a .
Calculation:
(2x3.16)² = (5.5)²+(5.5)²-2(5.5²) cos a
cos a = 20.56/60.5
a = 70.1degree
therefore, θ = 1.224 rad
After finding θ I used the formula:1/2 x (r)² (θ – sin θ) to calculate the area of the segment.
Calculation:
Area of segment=1/2 x 5.5)(1.224-sin70.1)
= 4.129cm2²
After all the calculation I manage to get 4.129cm² as the area of the segment.

For this part of the calculation I used formulas like area of circle, area of segment law of cosines. First I have to find the angle. So I used the law of cosine: a²= b² + c² - 2(b)(c) cos a to get the angle. Then in order to get the area of the inner circle, I multiply the area of the smaller circle by two and minus the area of the segment. Then to find the area of the shaded region, did the same thing for the outer circle. I calculated the area of the outer circle using the formula: πr² multiply it by two and minus the area of the bigger segment. From all the answers I got, took the area of the outer circle and minus the area of the inner circle. With that I have the answer of the shade region which is 191.02cm²

This is a picture of our model that we have created. I believe without the calculation of the model the shape of the object wouldn't turn our good. However with the skills of my members, we managed to complete the model together with the exact measurements. The assignment was tough because it took us quite some time to figure out the missing information and calculate every single measurement. We tried many mathematical formulas and law to calculate the whole object. I find this assignment very useful as I can open my mind and imagine the shape of the object and how it can be calculated. This skill can be useful for me as the time comes by. Mathematics can be applied in out daily life. that is why understanding and the ability to apply mathematics is very important.