SURVEYING PART 1 SURVEYING PART 2
LECTURE: SURVEYING Situation 2
1. A surveying instructor sent out six group of students to A line was determined to be 2395.25 m when measured
measure a distance between two points marked on the with a 30 m steel tape supported throughout its length
ground. The students come up with the following six under a pull of 4 kg at a mean temperature of 35⁰C. Tape
different values: 250.25, 250.15, 249.90, 251.04, 250.50, is used of standard length at 20⁰C under a pull of 5 kg.
and 251.22 meters. Assuming these values are equally Cross-sectional area of tape is 0.03 sq. cm. Coefficient of
reliable and that variations result from accidental errors, thermal expansion is 0.0000116/⁰C, Modulus of Elasticity
determine the most probable value of the distance of tape is 2 x 106 kg/cm2.
measured. 11. Determine the error of the tape due to change in
a. 250.51 m c. 252.34 m temperature.
b. 251.67 m d. 250.12 m a. 0.4963 m c. 0.4366 m
Situation 1 b. 0.4168 m d. 0.4519 m
The following values were determined in a series of tape 12. Determine the error due to tension.
measurements of a line: 1000.58, 1000.40, 1000.38, a. -0.0574 m c. -0.0399 m
1000.48, 1000.40, and 1000.46 m. Determine the ff: b. -0.1197 m d. -0.0985 m
2. Most probable value of the measured length. 13. Determine the corrected length of the line.
a. 1000.36 m c. 1000.45 m a. 2395.6269 m c. 2395.6478 m
b. 1000.72 m d. 1000.93 m b. 2395.6292 m d. 2395.5822 m
3. Probable error of a single measurement. Situation 3
a. ±0.07 m c. ±0.09 m A 50-m tape was standardized and was found to be 0.0042
b. ±0.01 m d. ±0.05 m m too long than the standard length at an observed
4. Probable error of the mean. temperature of 58⁰C and a pull of 15 kilos. The same tape
a. ±0.02 m c. ±0.04 m was used to measure a certain distance and was recorded
b. ±0.06 m d. ±0.08 m to be 673.92 m long at an observed temperature of 68⁰C
5. Relative precision of a single measurement. and a pull of 15 kilos. α = 11.6 x 10-6/⁰C.
a. 1/30000 c. 1/50000 14. Determine the standard temperature.
b. 1/20000 d. 1/70000 a. 50.76⁰C c. 45.780C
0
6. Relative precision of the mean. b. 52.36 C d. 47.960C
a. 1/30000 c. 1/50000 15. Determine the total correction.
b. 1/20000 d. 1/70000 a. 0.1473 m c. 0.1589 m
7. Four measurements of a distance were recorded as b. 0.1224 m d. 0.1348 m
284.18, 284.19, 284.22, and 284.20 meters and given 16. Determine the true length of the line.
weights of 1, 3, 2, and 4, respectively. Determine the a. 674.467 m c. 674.055 m
weighted mean. b. 674.843 m d. 674.152 m
a. 284.57 m c. 284.20 m Situation 4
b. 284.33 m d. 284.70 m A line is recorded as 472.90 m long. It is measured with a
8. It is desired to determine the most probable value of an 0.65 kg tape which is 30.005 m long at 20⁰C under a 50 N
angle which has been measured at different times by pull supported at both ends. During measurement, the
different observers with equal care. The values observed temperature is 5⁰C and the tape is suspended under a 75
were as follows: 74039’45’’ (in two measurements), N pull. The line is measured on 3% grade. E = 200 GPa, A =
74039’27’’ (in four measurements), and 74039’35’’ (in six 3 mm2 and α = 0.0000116/⁰C.
measurements). 17. Compute the actual length of tape during
a. 74039’34’’ c. 74039’57’’ measurement.
0
b. 74 39’21’’ d. 74039’40’’ a. 29.987 m c. 29.992 m
9. The three sides of a triangular-shaped tract of land is b. 29.645 m d. 29.302 m
given by the following measurements and corresponding 18. Compute the total error to be corrected for the
probable errors: a = 162.54 ± 0.03 m, b = 234.26 ± 0.05 inclined distance.
m, c = 195.70 ± 0.04 m. Determine the probable error of a. 0.134 m c. 0.157 m
the perimeter. b. 0.118 m d. 0.126 m
a. 0.09 m c. 0.10 m 19. What is the true horizontal distance?
b. 0.02 m d. 0.07 m a. 472.561 m c. 473.775 m
10. The two sides of a rectangular lot were measured with b. 472.819 m d. 473.986 m
certain estimated probable errors as follows: W = 253.36 Situation 5
± 0.06 m, and L = 624.15 ± 0.08 m. Determine the area of A steel tape with coefficient of linear expansion of
the probable error in the area of the lot. 0.0000116 per degree centigrade is known to be 50 m long
a. 43.26 m c. 43.97 m at 20⁰C. The tape was used to measure a line which was
b. 42.58 m d. 42.51 m found to be 532.28 m long when the temperature was
35⁰C. Determine the ff:
20. Temperature correction per tape length.
a. 0.0069 m c. 0.0037 m
b. 0.0087 m d. 0.0094 m 31. With the instrument still at P, determine the correct
21. Temperature correction for the measured line. reading on the far rod held at B for a horizontal line of
a. 0.0926 m c. 0.0457 m sight.
b. 0.1149 m d. 0.1036 m a. 2.243 m c. 2.178 m
22. Corrected length of the line. b. 2.641 m d. 2.490 m
a. 532.3726 m c. 533.1452 m 32. With the instrument still at P, determine the error in
b. 533.6714 m d. 532.9745 m the rod reading on the near rod held at A.
Situation 6 a. 0.0034 m c. 0.0023 m
A 45-m course, AB, on level ground was paced by a b. 0.0008 m d. 0.0012 m
surveyor for the purpose of determining his pace factor. 33. With the instrument still at P, determine the correct
The number of paces for each trial taken are 50, 53, 51, 53, reading on the near rod held at A for a horizontal line of
52, and 53. sight.
23. Determine his pace factor. a. 1.564 m c. 1.578 m
a. 0.762 m/pace c. 0.865 m/pace b. 1.449 m d. 1.671 m
b. 0.589 m/pace d. 0.613 m/pace
24. If the surveyor then took 771, 770, 768, 770, 772, and
SURVEYING PART 3
769 paces in walking an unknown distance CD, what is the Situation 8
length of the line? From the given data of a differential leveling as shown in
a. 666.10 m c. 664.50 m the tabulation:
b. 663.20 m d. 664.80 m STA BS HI FS ELEV
25. Assuming that the taped length of line CD is 667.0 m, BM1 1.256 127.133 m
TP1 1.116 1.886
determine the relative precision of the measurement
TP2 1.228 1.527
performed.
BM2 1.189 2.246
a. 1/500 c. 1/800
BM3 1.070 2.017
b. 1/600 d. 1/700 TP3 1.831 2.656
Situation 7 BM4 2.765
In the two-peg test of a dumpy level, the following 34. Determine the elevation of BM3.
observations were taken: a. 125.074 m c. 124.246 m
Rod Instrument Set Up Instrument Set Up b. 121.726 m d. 126.503 m
Reading Near A Near B 35. Find the difference in elevation between TP3 and BM4.
On point A 1.505 m 0.938 m a. 1.158 m c. 0.875 m
On point B 2.054 m 1.449 m b. 0.934 m d. 1.208 m
26. What is the difference in elevation between A and B?
Situation 9
a. 0.57 m c. 0.59 m
Complete the following differential level notes for a
b. 0.53 m d. 0.64 m
double-rodded line from BM1 to BM2.
27. If the line of sight is not in adjustment, determine the
STA BS HI FS ELEV
correct rod reading on A with the instrument still set up
BM1 1.964 205.549
near B. 1.964
a. 0.919 m c. 0.875 m TP1 – H 2.187 1.104
b. 0.963 m d. 0.847 m TP1 – L 2.629 1.549
28. Determine the error in the line of sight. TP2 – H 1.393 1.794
a. 0.019 m c. 0.036 m TP2 – L 1.780 2.202
b. 0.027 m d. 0.045 m TP3 – H 0.317 2.991
TP3 – L 0.741 3.415
Situation 8
BM2 2.634
In the two-peg test of a dumpy level using alternate
2.634
method, the following observations are taken: 36. Determine the elevation of BM2.
Rod Instrument Set Up Instrument Set Up a. 204.145 m c. 202.875 m
Reading Near M Near P
b. 206.395 m d. 201.175 m
On point A 0.296 m 1.563 m
37. Determine the difference in elevation between TP 1 and
On point B 0.910 m 2.140 m
Point M is equidistant from both A and B, while P is 2.50 m TP2.
away from A along the extension of line AB and 79.27 m a. 0.56 m c. 0.32 m
from B. b. 0.77 m d. 0.41 m
29. Determine the true difference in elevation between Situation 10
points A and B. In leveling across a deep and wide river, reciprocal level
a. 0.723 m c. 0.784 m readings were taken between two points, X and Y, as
b. 0.667 m d. 0.614 m follows:
30. With the instrument still at P, determine the error in a) With instrument set up near X, the rod readings on X are
the rod reading on the far rod held at B. 1.283 and 1.285 meters; on the distant point Y, the rod
a. 0.038 m c. 0.046 m readings are 2.618, 2.619, 2.621, and 2.622 meters.
b. 0.042 m d. 0.035 m b) With instrument set up near Y, the rod readings on Y are
3.478 and 3.476 meters; on the distant point X, the rod
readings are 2.143, 2.140, 2.146, and 2.144 meters.
38. Determine the true difference in elevation between Mirador hill with an elevation of 626 m is on a line
the two points. between Aurora hill whose elvation is 660 m and Cathedral
a. 1.335 m c. 1.475 m hill having an elevation of 600 m. The distance of Mirador
b. 1.265 m d. 1.135 m hill from Aurora hill is 10 km and the distance of Mirador
39. Determine the elevation of Y if the known elevation of hill from Cathedral hill is 12 km. Considering the effects of
X is 290.082 meters. curvature and refraction:
a. 288.747 m c. 290.364 m 47. Compute the obstruction of the line of sight at Mirador
b. 289.476 m d. 287.545 m hill when observing Cathedral hill from Aurora hill.
a. 0.49 m c. 0.96 m
b. 1.31 m d. 1.76 m
40. A vertical angle of -12025’ is measured to the top of a
water tank from an instrument set up on a hill 585 m away
from it. The telescope of the instrument is 1.45 m above 48. What would be the height of equal towers to be
the ground whose elevation is 462.73 m. Making due erected at Aurora hill and Cathedral hill so that Cathedral
allowance for the earth’s curvature and atmospheric hill, Aurora hill, and Mirador hill will be intervisible with a 4
refraction, determine the elevation of the base of the m tower erected at the top of Mirador hill?
water tank if the tank is 32 m high. a. 5.31 m c. 6.77 m
a. 341.20 m c. 326.70 m b. 4.36 m d. 7.34 m
b. 315.30 m d. 303.40 m 49. If no tower will be erected at Aurora hill and Mirador
hill, what would be the height of tower to be erected at
Cathedral hill so that Mirador and Cathedral hill will be
SURVEYING PART 4 intervisible from Aurora hill?
41. Two points, A and B, are 525.850 m apart. A level is set a. 3.13 m c. 4.73 m
up on the line between A and B and at a distance of 240.50 b. 1.20 m d. 2.89 m
m from A. If the rod reading on A is 3.455 m and that on B
is 2.806 m, determine the difference in elevation between
the two points, taking into account the effects of curvature
and atmospheric refraction.
a. 0.52 m c. 0.88 m
b. 0.37 m d. 0.65 m
42. A man on shore standing close to the sea’s water edge
looks out toward the direction of the sea. If his eyes
measure 1.72 m above sea level, determine how far out to
sea is his visible horizon, neglecting the effect of waves.
a. 4.36 km c. 5.94 km
b. 5.05 km d. 4.67 km
43. A woman standing on a beach can just see the top of a
lighthouse 24.140 km away. If her eye is 1.738 m above
sea level, determine the height of the lighthouse above
sea level.
a. 28.69 m c. 24.54 m
b. 31.03 m d. 26.45 m
Situation 11
Two hills A and C have elevations of 600 m and 800 m
respectively. In between A and C is another hill B which
has an elevation of 705 m and is located at 12 km from A
and 10 km from C.
44. Determine the clearance or obstruction of the line of
sight at hill B if the observer is at A so that C will be visible
from A.
a. 3.95 m c. 2.54 m
b. 1.87 m d. 4.63 m
45. If C is not visible from A, what height of tower must be
constructed at C so that it could be visible from A with the
line of sight having a clearance of 2 m above hill B.
a. 13.23 m c. 11.46 m
b. 9.78 m d. 10.91 m
46. What height of equal towers at A and C must be
constructed in order that A, B, and C will be intervisible.
a. 3.95 m c. 6.57 m
b. 2.41 m d. 1.96 m
Situation 12
