University Surveying Assignment 1: SVY2105, Semester 1, 2019

This document provides a comprehensive solution to SVY2105 Assignment 1, a civil engineering surveying assignment. The solution includes detailed calculations for the volume and standard deviation of a cylinder, considering measured height and diameter with associated errors. It also addresses the calculation of height differences using slope distance and zenith angle measurements, incorporating error analysis. Furthermore, the assignment delves into probability calculations involving a normally distributed random variable, determining probabilities within specified ranges and absolute values. Finally, it provides a solution for angle corrections and error analysis in surveying measurements. The solution demonstrates the application of surveying principles and mathematical concepts to solve practical problems, making it a valuable resource for students studying civil engineering and surveying.

Ans1.(a)
v+ ∆ v =π ( d+∆
2 )∗(h± ∆ h)
¿ π ¿
¿ π ¿
¿ π ¿
v+∆ v =3.99.012 ± 2.12%
∆ v=399.012∗2.12/100
∆ v=8.45 m3
Ans(c)
μ=1, σ =2
(1) P(1<x<6)
z-score = 1- 1−μ
σ = 1−1
2 =0
z-score2 = 1−μ
σ = 6−1
2 =2.5
0<z<2.5 = 0.99379-5.0000=0.49379

(2) P(x<-2.5)
z-score2 = 1−μ
σ = 1−(−2.5)
2 =1.75
=1- p(z>1.75)
=1 – 0.95994
= 0.04006
(3) P(-1.5<x<4.5)
z-score1=1.25
z-score2=1.75
=p(1.25<z<1.75)
=1- p(z>1.75) – p(z>1.25)
=1- 0.04006 -0.10565
=0.85429
(4) P(|x|>0.5)
=1-(-2<z<2)
=1-0.75
=0.25
(5) P(|X|<0.4)
=1-(-1.75<z<1.75)
=0.44066

Ans4
Angle 1 = 51°15´18" ± 8"
Angle 2 = 92°14´36" ± 7"
Angle 3 = 146°19´49" ± 6"
Angle 4 = 70°10´37" ± 8"
Angle 5 = 213°39´56" ± 8"
Angle 6 = 216°30´21" ± 6"
_______________________
788°127´271" ± 43"
--------------------------- = 131°41´46.167" ± 7.16"
6
The most probable values for the six angles=131°41´46.167" ± 7.16"
Error= 720°127´271" - 788°127´271"
= -68°127´271"
A:B:C:D:E:F =64:49:36:64:64:36 ------------------------(1)
A+B+C+D+E+F= -68°127´271" ----------------(2)
B=49/64 A ………………………………………(I)
C=36/64 A ………………………………………(II)
D=64/64 A ………………………………………(III)
E=64/64 A ………………………………………(IV)
F=49/64 A ………………………………………(V)
Put in equation (2)
A+ (49/64) A +(36/64) A +A+A +(36/64)A = -68°127´271"
A.488 = -68°127´271"
A.488 = -70.1769 °
A= -14°22´49.877"
A= -16.176944 degree
B = -12°22´ 40 .120"
D=--14°22´49.877"
C= --9°3´32.720"

E=-14°22´49.877"
F= -9°3´32.720"
Corrected angle
A =51.225° - 16.1769
A =35.0781
Corrected angle
F= 216.5058 – 9.0590 = 207.446°
B = 92.2433° - 12.2944° = 79.9489°
C = 146.33027° - 9.0590° = 137.27127°
D = 70.1769 ° -16.17694 =54.0009°
E= 213.6655° - 16.17694° = 197.4895°