Simpson\'s rule and Trapezoidal rule based on the following data: You are asked
ID: 1920911 • Letter: S
Question
Simpson's rule and Trapezoidal rule based on the following data:
You are asked to calculate an area for a land parcel bounded by a creek. Calculate the area by Simpson's rule Trapezoidal Rule, based on the following data: Which method would you prefer to calculate the area and why? A 20 m Times 20 m grid is set out over a total area of 40 m Times 40 m. Levels are taken on the grid and RL's calculated as follows: Levels are taken on the grid intersections and the RL's calculated, as below: The area is then cut to RL 680.5 m; calculate the volume of cut using grid levelling formulae. Determine the area of the following closed traverse (negligible mlsclose - do not Bowditch adjust) by the Double Areas method. Complete the table provided and show all workings to four decimal places.Explanation / Answer
a).
Simpson's rule:
A = (d/3)* [(h1 +h7) +4*(h2 +h4 +h6) +2*(h3 +h5)]
=> A = (10/3)* [(21 +22) +4*(24 +25 +17) +2*(27 +16)]
=> A = (10/3)* [43 +264 +86]
=> A = 1310 m^2
Trapezoidal Rule:
A = d*[(h1 +h7)/2 +h2 +h3 +h4 +h5 +h6]
=> A = 10* [(21+22)/2 +24 +27 +25 +16 +17]
=> A = 1305 m^2
We should prefer Simpson's rule because it gives a much accurate result.
b).
V1 = s^2 *[(1A -680.5) +(1B -680.5) +(2A -680.5) +(2B -680.5)]/4
=> V1 = 20*20*[13.6 +11.48 +18.15 +17.17]/4
=> V1 = 6040 m^3
V2 = s^2 *[(1B -680.5) +(1C -680.5) +(2B -680.5) +(2C -680.5)]/4
=> V2 = 20*20*[11.48 +4.96 +17.17 +17.28]/4
=> V2 = 5089 m^3
V3 = s^2 *[(2A -680.5) +(2B -680.5) +(3A -680.5) +(3B -680.5)]/4
=> V3 = 20*20*[18.15 +17.17 +16.04 +7.72]/4
=> V3 = 5908 m^3
V4 = s^2 *[(2B -680.5) +(2C -680.5) +(3B -680.5) +(3C -680.5)]/4
=> V4 = 20*20*[17.17 +17.28 +7.72 +12.64]/4
=> V4 = 5481 m^3
So, total volume = V1 +V2 +V3 +V4 = 22518 m^3