Pt1420 Unit 2 Assignment

Part A of Task Two requires the designing of a pool that incorporates three levels of depth and curves. These criteria are met by using three different polynomials, each with their own limits. These polynomials are designed so that they each fit together evenly. The polynomials are: -(x+1.241)^5-2.149 using the limits {-2.149 ≤ y ≤ 0} (x-1.759)(1/4 (x-0.959)) (x+1.241)^2-2.149 using the limits {-1.241 ≤ x ≤ 0} x^3/10-1.5 using the limits {-1.5 ≤ y ≤ 0}
When plotted, the curves will give a cross section of the pool. This cross section can be seen below in Figure 5. The blue section is Equation 1, the red is Equation 2, and the purple is Equation 3.
Figure 6. Cross section of the designed pool.
All of the points that can be seen on Figure …show more content…
After Analysis
Assumptions
The first assumption for this task, is that the pool, from an aerial perspective, is rectangular, and the side that is not seen on the cross-section is 10 metres long. That is, the pool is 10 metres long, with the width being the distance between the leftmost point of Equation 1, and the rightmost point of Equation 2, which is 4.872 metres long. If this assumption is wrong, and the pool is not rectangular, a different method of calculation would be needed to determine the volume of the pool.
The second assumption, is that there are no limits on the size of the pool, and, if there were, that this design would not exceed such limits. If this were to happen, the design would need to be altered in either design or scale, as to ensure the pool did not surpass given limits.
Similarly, the third assumption is that the design was accepted, no matter the aesthetics. This means that, despite the pool being an odd shape, Sugar World had no problems with the new design.
Strengths
The use of integration techniques and mathematical modelling to accurately plot a cross section, and then determine its area. Furthermore, the use of mathematical reasoning to assist in the calculation of the total volume of an irregular three-dimensional object, given the area of one of its

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