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Question 1
ప్రశ్న 1
In earthwork computation for a proposed road, which statement correctly distinguishes existing ground level (GL) from formation level (FL)?
Explanation:
Ground level represents the elevation of the existing terrain at a specified location. Formation level represents the proposed design elevation of the earthwork surface at that location. Both levels can be expressed as reduced levels relative to a common datum. Comparing these elevations helps determine whether cutting or filling is required. The difference between the levels provides the corresponding depth of earthwork. Formation levels must be interpreted according to the specified design profile rather than assumed to be identical to existing ground levels.
వివరణ:
Question 2
ప్రశ్న 2
At a particular chainage, the existing ground level is RL 104.65 m and the proposed formation level is RL 102.90 m. What type and depth of earthwork are required at the centre line?
Explanation:
The existing ground level is RL 104.65 m. The specified formation level is RL 102.90 m. Since the ground is higher than the proposed formation, material must be excavated. The depth of cutting is 104.65 - 102.90 = 1.75 m. Therefore the required earthwork is cutting to a depth of 1.75 m at the centre line. The calculation does not by itself establish the total cross-sectional area or volume of excavation.
వివరణ:
Question 3
ప్రశ్న 3
At a proposed embankment section, the existing ground level is RL 99.60 m and the formation level is RL 101.25 m. What is the required centre-line height of filling?
Explanation:
The formation level is higher than the existing ground level. Therefore the proposed construction requires filling rather than excavation. The filling height equals formation level minus ground level. Substituting the values gives 101.25 - 99.60 = 1.65 m. The required centre-line filling height is consequently 1.65 m. Additional data such as formation width, transverse ground profile and side slopes are required to determine the complete embankment area.
వివరణ:
Question 4
ప్రశ్న 4
Two successive survey stations on a pipeline alignment are marked at chainages 0+375 and 1+025. What is the horizontal chainage interval between these stations?
Explanation:
Chainage indicates the cumulative distance measured along a project alignment from its starting reference point. Chainage 0+375 represents a distance of 375 m. Chainage 1+025 represents a distance of 1,025 m. The interval is therefore 1,025 - 375 = 650 m. This distance may be used as the length between surveyed cross sections for earthwork computation. It should not be confused with the horizontal width of an individual cross section.
వివరణ:
Question 5
ప్రశ్న 5
Which statement correctly explains the respective purposes of longitudinal sections and cross sections in earthwork quantity estimation?
Explanation:
A longitudinal section represents ground elevations and proposed formation elevations along the direction of an alignment. It helps identify changes in cutting and filling along the project length. Cross sections describe the geometry of the ground and proposed earthwork across the alignment. Their transverse dimensions and levels are used to calculate sectional areas. The areas obtained at successive chainages provide the basis for computing earthwork volumes. Both types of sections are therefore important for reliable quantity estimation.
వివరణ:
Question 6
ప్రశ్న 6
The proposed formation level at chainage 0+100 is RL 108.40 m. The formation falls uniformly at a gradient of 1 in 250 towards chainage 0+350. What is the proposed formation level at chainage 0+350?
Explanation:
The longitudinal distance between the two chainages is 350 - 100 = 250 m. A falling gradient of 1 in 250 means that the formation elevation decreases by 1 m over a horizontal distance of 250 m. The vertical fall is therefore 250/250 = 1.00 m. Subtracting this fall from the initial formation level gives 108.40 - 1.00 = RL 107.40 m. Thus the required formation level at chainage 0+350 is RL 107.40 m. The ground level at that location would still be needed to determine the corresponding depth of cutting or filling.
వివరణ:
Question 7
ప్రశ్న 7
At chainage 0+000, the ground level is RL 102.40 m and the formation level is RL 101.60 m. At chainage 0+040, the ground level is RL 102.00 m and the formation level is RL 101.80 m. Which pair correctly gives the centre-line cutting depths at these two stations?
Explanation:
At the first station, the existing ground is higher than the proposed formation. Its cutting depth is 102.40 - 101.60 = 0.80 m. At the second station, the cutting depth is 102.00 - 101.80 = 0.20 m. Both differences indicate cutting because the ground level exceeds the formation level at each station. The cutting depth decreases along the specified 40 m interval. Determination of the volume between these stations additionally requires the cross-sectional geometry and an appropriate volume-computation method.
వివరణ:
Question 8
ప్రశ్న 8
A transverse survey across a proposed road formation shows that existing ground lies above formation on one side and below formation on the other. Which principle should be followed when computing the cross-sectional earthwork?
Explanation:
A transverse section can contain both cutting and filling when the existing ground crosses the proposed formation profile. The intersection separates the portion requiring excavation from the portion requiring embankment. The geometry of each portion should be measured individually. Cutting area and filling area represent different construction quantities and should not be arbitrarily combined into one net area. Separate calculations also support correct application of excavation, filling and compaction requirements. The corresponding quantities can later be reconciled for material reuse or disposal planning.
వివరణ:
Question 9
ప్రశ్న 9
A trench has a rectangular cross section with vertical sides, a uniform bottom width of 5.50 m and an excavation depth of 1.80 m. Assuming a level ground surface and no additional excavation width, what is its cross-sectional cutting area?
Explanation:
The trench has vertical sides and a rectangular cross section. For a rectangle, the sectional area equals width multiplied by depth. The specified bottom width is 5.50 m and the depth is 1.80 m. Therefore the area is 5.50 x 1.80 = 9.90 m2. No additional triangular side-slope areas are included because the sides are expressly stated to be vertical. The excavation volume over a known uniform length can subsequently be obtained by multiplying this area by that length.
వివరణ:
Question 10
ప్రశ్న 10
A road cutting has a formation width of 8.00 m and a centre-line depth of 2.00 m on level transverse ground. The cutting side slopes are 1.5 horizontal to 1 vertical on BOTH sides. What is the total cross-sectional area of cutting?
Explanation:
For a symmetrical cutting on level transverse ground, the sectional area is A = Bd + md^2. Here B is the formation width, d is the cutting depth and m is the horizontal side-slope ratio for one unit of vertical rise. Substituting B = 8.00 m, d = 2.00 m and m = 1.5 gives A = 8 x 2 + 1.5 x 2^2. The rectangular portion contributes 16.00 m2, while the two side-slope triangles together contribute 6.00 m2. The total cutting area is therefore 22.00 m2. The expression assumes identical side slopes and a level transverse ground surface.
వివరణ:
Question 11
ప్రశ్న 11
A symmetrical road embankment is constructed over level transverse ground with a formation width of 7.00 m and a filling height of 1.50 m. Both embankment side slopes are 2 horizontal to 1 vertical. What is the total width between the toes of the embankment?
Explanation:
The formation width is the horizontal width at the top of the embankment. A side slope of 2 horizontal to 1 vertical produces a horizontal extension of twice the filling height on each side. For a filling height of 1.50 m, the horizontal extension on one side is 2 x 1.50 = 3.00 m. Both side slopes together contribute 6.00 m to the total width. Adding this to the formation width gives 7.00 + 6.00 = 13.00 m. The calculated width is measured between the two embankment toes on the assumed level ground.
వివరణ:
Question 12
ప్రశ్న 12
A trapezoidal earthwork cross section has a bottom width of 6.00 m, a top width of 14.00 m and a vertical depth of 2.00 m. What is its cross-sectional area?
Explanation:
The area of a trapezoid equals one-half of the sum of its parallel sides multiplied by the perpendicular distance between them. The two parallel widths are 6.00 m and 14.00 m. Their sum is 20.00 m. The area is therefore (6.00 + 14.00) x 2.00/2 = 20.00 m2. This formula is suitable when the earthwork section has the stated trapezoidal geometry. Multiplication by a uniform longitudinal length would give the corresponding prismatic earthwork volume.
వివరణ:
Question 13
ప్రశ్న 13
A 6.00 m wide earthwork strip has vertical lateral boundaries. At transverse offsets of 0 m, 3 m and 6 m, the measured cutting depths below a horizontal formation line are 0.60 m, 1.20 m and 0.80 m respectively. Assuming the existing ground varies linearly between successive offsets, what is the total cutting area across the strip?
Explanation:
The measured transverse section is divided into two strips, each 3.00 m wide. The cutting depth varies linearly between the specified offsets, so the trapezoidal-area rule can be applied to each strip. The first strip has an area of (0.60 + 1.20) x 3.00/2 = 2.70 m2. The second strip has an area of (1.20 + 0.80) x 3.00/2 = 3.00 m2. Adding these areas gives 2.70 + 3.00 = 5.70 m2. No additional exterior side-slope areas are included because the question specifies vertical lateral boundaries.
వివరణ:
Question 14
ప్రశ్న 14
Two consecutive earthwork cross sections are 25.00 m apart. Their cutting areas are 12.00 m2 and 18.00 m2 respectively. Using the average-end-area method, what is the estimated volume of cutting between them?
Explanation:
The average-end-area method estimates volume using the arithmetic mean of two consecutive sectional areas. The first area is 12.00 m2 and the second area is 18.00 m2. Their average is (12.00 + 18.00)/2 = 15.00 m2. The distance between the sections is 25.00 m. Therefore the estimated cutting volume is 15.00 x 25.00 = 375 m3. This method is commonly applied where sectional areas change reasonably smoothly between successive survey stations.
వివరణ:
Question 15
ప్రశ్న 15
Earthwork cross-sectional areas at chainages 0+000, 0+020 and 0+040 are 10 m2, 14 m2 and 18 m2 respectively. Using the average-end-area method separately for the two 20 m intervals, what is the total estimated earthwork volume?
Explanation:
The three survey stations define two equal intervals of 20 m each. For the first interval, the average sectional area is (10 + 14)/2 = 12 m2. The first interval volume is therefore 12 x 20 = 240 m3. For the second interval, the average area is (14 + 18)/2 = 16 m2, producing 16 x 20 = 320 m3. The total volume is 240 + 320 = 560 m3. The middle sectional area contributes to both adjoining intervals and must be accounted for accordingly.
వివరణ:
Question 16
ప్రశ్న 16
For a 30.00 m long earthwork reach, the cross-sectional area at the beginning is 12 m2, the area at the exact midpoint is 19 m2 and the area at the end is 24 m2. What is the earthwork volume computed using the prismoidal formula?
Explanation:
The prismoidal formula is V = L(A1 + 4Am + A2)/6. In this expression A1 and A2 are the end areas and Am is the area at the midpoint. The given values are L = 30.00 m, A1 = 12 m2, Am = 19 m2 and A2 = 24 m2. Substitution gives V = 30(12 + 4 x 19 + 24)/6. The expression inside the brackets is 112. Therefore the volume is 30 x 112/6 = 560 m3 under the stated prismoidal computation.
వివరణ:
Question 17
ప్రశ్న 17
A road embankment has a constant formation width of 8.00 m, side slopes of 1 horizontal to 1 vertical on both sides, and filling heights of 1.00 m and 3.00 m at two sections 20.00 m apart. Assuming the transverse ground is level at each section and the longitudinal filling depth varies linearly, what volume is obtained by the MID-SECTIONAL AREA method?
Explanation:
The mid-sectional area method uses the cross-sectional area corresponding to the mean depth between the two stations. The mean filling depth is (1.00 + 3.00)/2 = 2.00 m. For level transverse ground with symmetrical side slopes, the sectional area is A = Bd + md^2. Substituting B = 8.00 m, d = 2.00 m and m = 1 gives A = 8 x 2 + 1 x 2^2 = 20.00 m2. Multiplying by the length of 20.00 m gives V = 20.00 x 20.00 = 400 m3. This is the result of the specified mid-sectional method rather than the average-end-area method.
వివరణ:
Question 18
ప్రశ్న 18
A road embankment has a formation width of 8.00 m, symmetrical side slopes of 1 horizontal to 1 vertical and filling heights of 1.00 m and 3.00 m at the ends of a 20.00 m reach. The transverse ground is level at both sections. What volume is obtained by the AVERAGE-END-AREA method?
Explanation:
The average-end-area method requires the complete sectional area at each end of the reach. For the first section, A1 = 8 x 1 + 1 x 1^2 = 9.00 m2. For the second section, A2 = 8 x 3 + 1 x 3^2 = 33.00 m2. The arithmetic mean of the end areas is (9.00 + 33.00)/2 = 21.00 m2. Multiplying by the section spacing gives V = 21.00 x 20.00 = 420 m3. The result differs from the mid-sectional method because the side-slope contribution to area varies quadratically with filling depth.
వివరణ:
Question 19
ప్రశ్న 19
A proposed horizontal formation line crosses an irregular transverse ground profile. Over the first 2.00 m of a surveyed strip, the cutting depth decreases linearly from 0.80 m to zero. Over the next 3.00 m, the filling depth increases linearly from zero to 0.60 m. The strip boundaries are vertical and exterior side slopes are excluded. What are the separate cutting and filling areas?
Explanation:
The ground profile crosses the formation line at the boundary between the two stated strips. The first strip is triangular in section because its cutting depth decreases linearly from 0.80 m to zero. Its cutting area is 2.00 x 0.80/2 = 0.80 m2. The second strip is also triangular, with a filling depth increasing from zero to 0.60 m over 3.00 m. Its filling area is 3.00 x 0.60/2 = 0.90 m2. These two areas must be recorded separately because they represent excavation and embankment quantities respectively.
వివరణ:
Question 20
ప్రశ్న 20
Earthwork cross-sectional areas at chainages 0+000, 0+030 and 0+075 are 8 m2, 12 m2 and 16 m2 respectively. Using the average-end-area method and the ACTUAL spacing of each interval, what is the total estimated volume?
Explanation:
The distance from chainage 0+000 to 0+030 is 30 m. The distance from 0+030 to 0+075 is 45 m. The first interval volume is (8 + 12)/2 x 30 = 300 m3. The second interval volume is (12 + 16)/2 x 45 = 630 m3. Adding the two interval volumes gives 300 + 630 = 930 m3. It would be incorrect to apply a single assumed 30 m interval throughout because the survey stations are unequally spaced.
వివరణ:
Question 21
ప్రశ్న 21
A straight embankment of uniform cross section is 40.00 m long. Its formation width is 7.00 m, filling height is 1.50 m, and both side slopes are 1 horizontal to 1 vertical over level transverse ground. What is its theoretical compacted earthwork volume?
Explanation:
For a symmetrical embankment on level transverse ground, sectional area is A = Bd + md^2. The formation width is 7.00 m and the filling height is 1.50 m. Both side slopes have a horizontal-to-vertical ratio of 1, so m = 1. The sectional area is 7 x 1.50 + 1 x 1.50^2 = 10.50 + 2.25 = 12.75 m2. Since the cross section is uniform along the 40.00 m length, volume is 12.75 x 40.00 = 510 m3. The result represents the theoretical in-place embankment geometry without applying a separate loose-material conversion factor.
వివరణ:
Question 22
ప్రశ్న 22
A road cutting is formed on level transverse ground with a bottom formation width of 5.00 m and a vertical cutting depth of 1.50 m. The side slopes on both sides are 1 vertical to 2 horizontal. What is the total top width of the cutting between the ground intercepts?
Explanation:
A side slope of 1 vertical to 2 horizontal gives a horizontal projection of twice the vertical depth. The specified cutting depth is 1.50 m. Therefore the horizontal extension on each side is 2 x 1.50 = 3.00 m. The two sides together contribute 6.00 m to the cutting width. Adding the bottom formation width gives 5.00 + 6.00 = 11.00 m. This top width assumes a level transverse ground surface and identical cutting side slopes.
వివరణ:
Question 23
ప్రశ్న 23
A road excavation produces 125 m3 of usable earth measured in situ. Under the expressly stated project assumption, every 1.00 m3 of usable in-situ excavated soil yields 0.80 m3 of completed compacted embankment. If the required completed embankment volume is 110 m3, what is the shortfall expressed as COMPACTED fill volume?
Explanation:
The available excavated quantity is 125 m3 measured in its original in-situ condition. The question specifies a compacted-volume yield factor of 0.80. Therefore the estimated completed embankment volume obtainable from this material is 125 x 0.80 = 100 m3. The required completed embankment volume is 110 m3. The compacted fill shortfall is 110 - 100 = 10 m3. This value must not be interpreted directly as the loose borrow-material requirement without a separate conversion assumption.
వివరణ:
Question 24
ప్రశ్న 24
At chainage 0+000, the existing ground level is RL 102.60 m and the formation level is RL 101.80 m. At chainage 0+050, the ground level is RL 101.00 m and the formation level is RL 102.20 m. Assuming both ground and formation levels vary LINEARLY between these stations, at what chainage does the centre-line cutting change to filling?
Explanation:
At chainage 0+000, the ground exceeds the formation by 102.60 - 101.80 = 0.80 m, indicating cutting. At chainage 0+050, the formation exceeds the ground by 102.20 - 101.00 = 1.20 m, indicating filling. The total change in the signed ground-minus-formation difference is 0.80 + 1.20 = 2.00 m. Since both longitudinal profiles vary linearly, the zero-depth point occurs at a fraction 0.80/2.00 of the 50 m interval. The distance from the first station is therefore 50 x 0.80/2.00 = 20 m. Consequently, the centre-line transition occurs at chainage 0+020.
వివరణ:
Question 25
ప్రశ్న 25
A road section has a cutting area of 20 m2 at chainage 0+000, zero earthwork area at chainage 0+020, and a filling area of 16 m2 at chainage 0+040. The cutting and filling portions are assumed to vary sufficiently for separate average-end-area calculations over their respective 20 m reaches. What are the estimated cutting and filling volumes respectively?
Explanation:
The zero-area station at chainage 0+020 separates the cutting and filling reaches. For the first 20 m interval, cutting area decreases from 20 m2 to zero. The estimated cutting volume is (20 + 0)/2 x 20 = 200 m3. For the second 20 m interval, filling area increases from zero to 16 m2. The estimated filling volume is (0 + 16)/2 x 20 = 160 m3. The two quantities must be recorded separately rather than reduced to a single net cutting volume, because excavation and embankment are distinct measurable operations.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. Ground level represents the existing ground elevation, while formation level represents the specified elevation to which earthwork is to be brought. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: C. Cutting of 1.75 m. సమాధానం: C.
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Question 3 ప్రశ్న 3Answer: A. 1.65 m. సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: D. 650 m. సమాధానం: D.
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Question 5 ప్రశ్న 5Answer: C. A longitudinal section shows ground and formation profiles along the alignment, while cross sections represent transverse ground and formation geometry at selected chainages. సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: A. RL 107.40 m. సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: B. 0.80 m cutting and 0.20 m cutting. సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: D. Identify the transition point and compute cutting and filling areas separately within the same cross section. సమాధానం: D.
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Question 9 ప్రశ్న 9Answer: B. 9.90 m2. సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: C. 22.00 m2. సమాధానం: C.
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Question 11 ప్రశ్న 11Answer: D. 13.00 m. సమాధానం: D.
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Question 12 ప్రశ్న 12Answer: A. 20.00 m2. సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: C. 5.70 m2. సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: B. 375 m3. సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: D. 560 m3. సమాధానం: D.
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Question 16 ప్రశ్న 16Answer: A. 560 m3. సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: B. 400 m3. సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: C. 420 m3. సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: A. Cutting 0.80 m2 and filling 0.90 m2. సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: D. 930 m3. సమాధానం: D.
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Question 21 ప్రశ్న 21Answer: C. 510 m3. సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: B. 11.00 m. సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: D. 10 m3. సమాధానం: D.
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Question 24 ప్రశ్న 24Answer: A. 0+020. సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: B. 200 m3 cutting and 160 m3 filling. సమాధానం: B.
