This document contains 21 multi-part surveying problems involving calculating true distances and areas from measurements taken using chains of various lengths that may have been inaccurate. The problems require applying formulas to account for errors in the chains and scaling of maps in order to determine the true values sought, such as distances between points or areas of land parcels.

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ASSIGNMENT NO. 2
SURVEYING
PROBLEMS ON CHAIN
To solve such problem
1) Lo = (
𝒍 𝟏
𝒍 𝟎
)
𝟐
Lo
2) Ao = (
𝒍 𝟏
𝒍 𝟎
)
𝟐
Ao
TYPE I) To calculate true distance
1. A 20 m chain was tested before the commencement of the day’s work and found to be correct.
After chaining 840 m the chain was found to be 0.08 m too long. At the end day’s work, after
chaining a total distance of 1376 m the chain was found to be 0.12 m too long. What was true
distance chained?
2. The distance between two points, measured with 20 m chain, was recorded as 327 m. It was
afterwards found that the chain was 3 cm too long. What was the true distance between the
points?
3. The distance between two stations was 1200 m when measured with a 20 m chain. The same
distance when measured with 30 m chain was found to be 1195 m. If the 20 m chain was 0.05 m
too long, what was the error in the 30 m chain?
TYPE II) To calculate true distance
1. The distance measured between two points by a 20m chain was 1340 m and when measured by a
30 m chain was 1345 m. If the 30 m chain was one link too short; find out if the 20m chain was
of correct length or not. If not find the error in it.
2. The lengths of 20 m and 30 m chains were tested and found to be correct at the beginning of
work. The distance between two points measured by 20 m chain was 1340 m and when measured
by 30 m chain was 1345 m. 30 m chain was tested again and found to be 20 cm too short.

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Calculate average chain length and final chain length of 20 m chain at the end of measurement.
(09 Mks)
3. A 30 m chain was found to be 15.24 cm too long after chaining 1524 m. The same chain was
found to be 30.48 cm too long after chaining a total distance of 3048 m. Find the correct length
of the total distance assuming chain was correct at the commencement of chaining.
4. A line was measured by 20 m chain which was accurate before starting the day’s work. After
chaining 900 m, the chain was found to be 6 cm too long. After chaining of 1575 m, the chain
was found to be 14 cm too long. Find the true distance of the line.
5. A 30 m chain (150 links) was found to be one link too short. The area measured with this chain
also plotted to scale 1 cm = 8 m and was found to be 32.659 cm2. The map was found to have
shrunk so that a line originally 10 cm long was only 9.8 cm. Find true area of the field. (09)
TYPE III) To calculate true area
1. A chain was tested before start and found to be 30 m. At the end of work it was checked again
and found to be 30.10 m. Area of plan drawn to a scale 1: 1000 was 160 sq. m. Find the true
area in hectres. (06 Mks)
2. A chain was tested before starting a survey of field and was found to be exactly 30 m. At the end
of the survey it was tested again and was found to measure 30.16 m. The area of plan drawn to a
scale of 1 cm = 60 m was 92.50 cm2. Find the true area of field. (Nov. 2011) 08 Mks
3. An old map was drawn with a scale of 1cm = 10 m, the field was surveyed with a 30 m chain
which was actually 0.05 m short. An original length of 10 cm has now shrunk to 9.5 cm on
drawing. The plan area measured with a planimeter is 95 cm2. Calculate the actual area of the
land.
4. A chain was tested before starting a survey of field and was found to be exactly 20 m. At the end
of the survey it was tested again and was found to measure 20.20 m. The area of plan drawn to a
scale of 1 cm = 80 m was 100 cm2. Find the true area of field.
5. A 30 m chain (150 links) was found to be one link too short. The area measured with this chain
also plotted to scale 1 cm = 8 m and was found to be 32.659 cm2. The map was found to have
shrunk so that a line originally 10 cm long was only 9.8 cm. Find true area of the field.
(09 marks)
6. An old map was drawn with a scale of 1cm = 8 m, but now the paper is found to have shrunk. A
line originally 200 mm long now measures 190 mm only. The area of a plot now measures 100.5

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cm2. There was also a note that the 30 m chain was 100 mm too short. Find the true area of the
plot.
7. A rectangular field was measured with a 30 m chain. Its length was found to be 3000 m and its
breadth 2500 m. before starting the work the chain was compared with a standard rope and was
found to be short by 5 cm. At the end of the work, the chain was found to be longer than the
standard length by 30 cm. What is the actual area of the field?
8. A 20 m chain was tested before the commencement of the day’s work and found to be correct.
After chaining 840 m the chain was found to be 0.08 m too long. At the end of the day’s work,
after chaining a total distance of 1376 m the chain was found to be 0.12m too long. What was the
true distance chained?
9. A chain was tested before starting a survey of field and was found to be exactly 30 m. At the end
of the survey it was tested again and was found to measure 30.16 m. The area of the plane drawn
to a scale of 1 cm = 60 m was 92.5 cm2. Find the area of the field.
10. A plan of an old survey plotted to a scale of 1 cm = 10 m was found to have shrunk so that a line
originally measuring 25 cm long was found to measure 24.4 cm. If the area of the plan measured
now is 122 cm2, determine the true area of the survey. Calculate shrinkage factor.
11. A old map was plotted to a scale of 40 m to 1cm.Over the years, this map has been shrinking,
and a line originally 20 cm long is only 19.5 cm long at present. Again the 20m chain was 5 cm
too long. If the present area of the map measured by planimeter is 125.50 cm2, find the true area
of land surveyed. ( 9)
12. The old map was drawn to a scale of 1cm = 8 m, but now the paper is found to have shrunk. A
line originally 200 mm long now measures 190mm only. The area of a plot now measures 100.5
cm2. There was also a note that the 30m chain used was 100 mm too short. Find the true area of
the plot.
13. A 20 m chain was tested before the commencement of the day's work and found to be correct.
After chaining 840 m the chain was found to be 0.08 m too long. At the end of day's work, after
chaining a total distance of 1376 m the chain was found to be 0.12 m too long. What was true
distance chained?
14. A chain was tested before start and found to be 30 m. At the end of work it was checked again
and found to be 30.20 m. The area of plan drawn to a scale of 1: 1000 was 200 sq. m. Find the
true area on field in hectares.
15. The area of a plan of an old map plotted to a scale of 1 m = 10 m. Measures 100 sq. m. The plan
is found to have shrunk so that the line originally 10 cm long now measures 9.7 cm, Further the

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20 m chain used was 8 cm too short. Find the true area of the survey.
16. A chain was tested before start and found to be 30 m. At the end of work it was checked again
and found to be 30.10 m. The area of plan drawn to a scale 1: 1000 was 160 sq .m. Find the true
area in hectres.
17. The old map was drawn to a scale of 1 em = 8 m, but now the paper is found to have shrunk. A
line originally 200 mm long now measures 190 mm only. The area of a plot now measures 100.5
cm-. There was also a note that the 30 m chain used was 100 mm too short. Find the true area of
the plot. (9)
18. A chain was tested before start and found to be 30 m. At the end of work it was checked again
and found to be 30.10 m. The area of plan drawn to a scale 1 : 1000 was 160 sq .m. Find the true
area in hectres.
19. The lengths of 20 m and 30 m chains were tested and found to be correct at the beginning of
work. The distance between two points measured by 20 m chain was 1340 m and when measured
by 30 m chain was 1345 m. 30 m chain was tested again and found to be 20 cm too short.
Calculate average chain length and final chain length of 20 m chain at the end of measurement.
20. The lengths of 20 m and 30 m chains were tested and found to be correct at the beginning of
work. The distance between two points measured by 20 m chain was 1340 m and when measured
by 30 m chain was 1345 m. 30 m chain was tested again and found to be 20 cm too short.
Calculate average chain length and final chain length of 20 m chain at the end of measurement.
21. Distance ABC was measured with a 30 m chain, tested and found to be correct in the
beginning of the work. After measuring AB = 1.2 kms, chain was found to be 10 cm
too long. Chaining was continued till total distance of 2.0 kms up to point C. At the
end of the work chain was found to be 20 cm too long. Find correct distance ABC.