Mathematics

Aerial View of the model

Side view of the model

Full view of the model

In this assignment, there were many theories used and combined to measure the total surface area of the model and also the accurate measurements needed to construct the model. 

As can be seen, the first step we took was to calculate the area of the upper part of the circle. To get this, the formulae for area of circle is used.  Putting the values in the formulae, the total area of the circle is 95.05 cm.  The second formulae used was the area of rectangle because there is a rectangle in the centre of the two circles. The area of the rectangle is 72 cm. After that, to find the area of intersection between the two circles in the centre, the law of cosine was used. the adjacent value of the triangle formed is divided with its hypotenuse value to get the angle at the centre. With this, the area of the sector of circles that intersects can be calculated. The area of sector was calculated the formulae and the value we obtained is 37.6 cm. Next, the area for the triangles formed by cutting through the circumference of the circle is calculated with the common formulae for the area of triangle. The area of the segments was calculated using the formulae and a figure was obtained. Subtracting the total area of the circles/cylinders with the total surface area of the segments in between the cicles, the value obtained is 109.48 cm.

The next step was to calculate the total surface are inside the combined cylinders. the shape inside is a pyramid. Firstly, the height and width of the pyramid has to be determined. This was done by using Phytogoras's Theorem and ratio to determine the hypotenuse (considered as the height of the triangle) and adjacent (considered as the width of the rectangle). After that, the opposite value to the triangle or also known as the slanted side of the triangle can be determined by the simple theorem. This will lead to  the determination of the total area of the pyramid in the centre. Next is to calculate the base area of the pyramid. This can be done easily because the area is already determined from calculating the adjacent values of the triangles and multiplying it by 2 to get the width and length of the base area. 

This shows the calculations of the outer surface area of the cylinder along with the surface are of the rims surrounding the conjoined cylinders. The surface area of the conjoined cylinders are divided into 2 sections. One was labeled as section A and the are below the rims are labeled as B. Combining the formulas, the surface area of A and B were determined. 

The total surface area of the model is calculated by adding all the surface area of the dismantled surfaces of the conjoined cylinders. 

REFLECTION

This assignment looked easy when we first received it. However, when it came to calculating and constructing the model, it proved to be one of the difficult and challenging assignment I have ever had to do. It combined the brain power of seven members and still it took a few days to complete. This assignment requires the creativity of the students to mix and make well used of the simple formulas that we have been thought and apply it int he calculations.