Reference no: EM132296470

Mathematics Project -

PART I: Trapezoidal Rule and Simpson's 1/3^rd Rule in finding approximate area

Trapezoidal rule and or Simpson's 1/3^rd rule are commonly used to find the approximate surface area of the lands or some irregular surfaces. In this project you need to design a small land of your choice. Then you need to find the area and volume by using Trapezoidal rule and or Simpson's 1/3^rd rule as indicated below.

1. To sketch the design of the project first you draw a quadrilateral (base of your land as shown in Fig 1. - attached) with side lengths of a, b, c and d units on a graph paper, where

a = 600 units + last 3 digits of your student number.

b = 450 units + last 3 digits of your student number.

c = 400 units + last 2 digits of your student number.

d = 350 units + last 2 digits of your student number.

(e.g. if your student number is 3654283 then a = 883, b = 733, c = 483, d = 433units respectively).

2. Estimate the area of the base of the land (quadrilateral), you sketched in (1), by using trapezoidal rule and Simpson's 1/3^rd rule with any number of strips (at least 8 strips) of your choice.

3. Now join the two end points of sides a, b, c and d of the quadrilateral you sketched in part (1), by irregular curves (an example is shown in Fig 2. - attached) to create the land of your choice named Student Land.

Now estimate these four areas (areas you sketched outside the four sides a, b, c and d of the quadrilateral) by using trapezoidal rule with 9 strips (if addition of your student number is an odd number) or by using Simpson's 1/3^rd rule with 10 strips (if addition of your student number is an even number). Hence estimate the total area of the land and conclude your findings.

Please note: Include drawing of Student Land (quadrilateral +extensions) and drawings of each irregular shape area.

PART II: Trapezoidal Rule and Simpson's 1/3^rd Rule in finding approximate volume

For transportation purposes undersea tunnel needs to be constructed to provide fast link between the Student Land and X-Land, see Figure 3 - attached.

A tunnel of length (a + 1000) unit (similar to the Fig 4. - attached) will be constructed to join the Student Land with X-Land. The eleven cross sectional areas at regular intervals are: S₀ = 100, S₁ = 112, S₂ = 115, S₃ = 117, S₄ = 119, S₅ = 121, S₆ = 123, S₇ = 126, S₈ = 128, S₉ = 131 and S₁₀ = 134.

Now estimate the volume of undersea tunnel by using trapezoidal rule with 10 strips and by using Simpson's 1/3^rd rule with 10 strips. Comment on your findings.

Note: All figures are in attached file. The figures are just shown as examples without considering the scales. You need to scale properly for all your graphs/sketches.

Attachment:- Assignment File.rar