Test 26 - Trapezoidal Method of Earthwork

Question 1 ప్రశ్న 1

For n successive earthwork cross sections having areas A1, A2, ..., An at equal longitudinal spacing d, which expression correctly gives the total volume by the composite trapezoidal method?

A V = d(A1 + A2 + ... + An). B V = (d/2)[A1 + An + 2(A2 + A3 + ... + A(n-1))]. C V = (d/3)[A1 + An + 4(A2 + A3 + ... + A(n-1))]. D V = d(A1 + An)/2, irrespective of the number of intermediate sections.

Question 2 ప్రశ్న 2

Two successive road-cutting cross sections have areas of 14 m2 and 26 m2. The longitudinal distance between the sections is 30 m. What is the estimated cutting volume using the trapezoidal method?

A 560 m3. B 620 m3. C 600 m3. D 780 m3.

Question 3 ప్రశ్న 3

Four consecutive earthwork cross sections have areas of 8 m2, 14 m2, 20 m2 and 12 m2. The longitudinal spacing between each pair of successive sections is 25 m. What is the total volume calculated using the trapezoidal rule?

A 1,000 m3. B 1,050 m3. C 1,150 m3. D 1,100 m3.

Question 4 ప్రశ్న 4

Five consecutive earthwork cross sections are spaced at uniform 20 m intervals. Their areas are 10 m2, 16 m2, 12 m2, 18 m2 and 24 m2 respectively. What is the estimated earthwork volume by the composite trapezoidal formula?

A 1,260 m3. B 1,200 m3. C 1,320 m3. D 1,380 m3.

Question 5 ప్రశ్న 5

Earthwork cross sections at chainages 0+000, 0+025, 0+065 and 0+090 have areas of 12 m2, 18 m2, 10 m2 and 20 m2 respectively. Using the trapezoidal method with the ACTUAL interval lengths, what is the total volume?

A 1,250 m3. B 1,310 m3. C 1,390 m3. D 1,450 m3.

Question 6 ప్రశ్న 6

Six consecutive cross sections of a canal excavation have areas of 6 m2, 10 m2, 14 m2, 18 m2, 22 m2 and 26 m2. Their longitudinal spacing is uniformly 15 m. What is the total excavation volume by the trapezoidal rule?

A 1,080 m3. B 1,170 m3. C 1,200 m3. D 1,260 m3.

Question 7 ప్రశ్న 7

Three equally spaced earthwork cross sections have areas of 8 m2, A m2 and 20 m2. The spacing is 25 m, and the total volume calculated by the trapezoidal method is 650 m3. What is the unknown intermediate sectional area A?

A 8 m2. B 10 m2. C 14 m2. D 12 m2.

Question 8 ప్రశ్న 8

Four consecutive earthwork sections have areas of 10 m2, 14 m2, 20 m2 and 16 m2. The sections are equally spaced, and their total trapezoidal volume is 1,175 m3. What is the common longitudinal interval?

A 25 m. B 20 m. C 30 m. D 35 m.

Question 9 ప్రశ్న 9

Two survey stations on a pipeline excavation alignment are situated at chainages 0+080 and 0+135. Their respective excavation cross-sectional areas are 9 m2 and 15 m2. What is the trapezoidal earthwork volume between these stations?

A 550 m3. B 660 m3. C 600 m3. D 720 m3.

Question 10 ప్రశ్న 10

A road embankment has a formation width of 8 m and symmetrical side slopes of 1.5 horizontal to 1 vertical over level transverse ground. The filling heights at two consecutive sections are 1 m and 2 m, with a longitudinal spacing of 30 m. What volume is obtained by the trapezoidal method?

A 450.0 m3. B 465.0 m3. C 472.5 m3. D 480.0 m3.

Question 11 ప్రశ్న 11

A cutting has a formation width of 6 m, a left side slope of 1 horizontal to 1 vertical and a right side slope of 2 horizontal to 1 vertical. The cutting depths at two consecutive sections are 1.5 m and 2.5 m over level transverse ground. If the interval is 20 m, what is the earthwork volume by the trapezoidal method?

A 350.0 m3. B 360.0 m3. C 375.0 m3. D 367.5 m3.

Question 12 ప్రశ్న 12

A straight excavation has vertical lateral boundaries. Its width is 5.0 m and depth is 1.2 m at the first section, while its width is 7.0 m and depth is 1.8 m at the second section. The longitudinal spacing is 40 m. What volume is estimated by the trapezoidal method?

A 372 m3. B 360 m3. C 384 m3. D 408 m3.

Question 13 ప్రశ్న 13

Two consecutive excavation sections have trapezoidal geometry. The first section has a bottom width of 6 m, a top width of 10 m and a depth of 2 m. The second section has a bottom width of 6 m, a top width of 14 m and a depth of 3 m. What is the trapezoidal-method volume if the sections are 30 m apart?

A 650 m3. B 690 m3. C 750 m3. D 820 m3.

Question 14 ప్రశ్న 14

Over a 50 m earthwork interval, the SIGNED cross-sectional area varies linearly from +15 m2 of cutting at the first section to -10 m2 of filling at the last section. Using the trapezoidal method separately before and after the zero-area transition, what are the cutting and filling volumes?

A 220 m3 cutting and 125 m3 filling. B 225 m3 cutting and 125 m3 filling. C 225 m3 cutting and 100 m3 filling. D 250 m3 cutting and 100 m3 filling.

Question 15 ప్రశ్న 15

Two consecutive 40 m-spaced cross sections each contain both cutting and filling. The first section has 6 m2 of cutting and 2 m2 of filling, while the second has 14 m2 of cutting and 8 m2 of filling. Assuming linear variation of the respective sectional areas, what are the trapezoidal cutting and filling volumes?

A 350 m3 cutting and 200 m3 filling. B 400 m3 cutting and 120 m3 filling. C 300 m3 cutting and 200 m3 filling. D 400 m3 cutting and 200 m3 filling.

Question 16 ప్రశ్న 16

At two consecutive excavation cross sections 50 m apart, the respective soil-cutting areas are 12 m2 and 18 m2, while the rock-cutting areas are 3 m2 and 5 m2. What are the SOIL and ROCK excavation quantities using the trapezoidal method separately for each material class?

A 750 m3 soil and 200 m3 rock. B 750 m3 soil and 125 m3 rock. C 800 m3 soil and 200 m3 rock. D 900 m3 soil and 250 m3 rock.

Question 17 ప్రశ్న 17

A cutting cross section has zero area at the beginning of a 30 m reach and an area of 24 m2 at the end. If the trapezoidal method is specifically prescribed, what is its ESTIMATED volume?

A 300 m3. B 360 m3. C 400 m3. D 720 m3.

Question 18 ప్రశ్న 18

For a 30 m earthwork interval, the end-sectional areas are 10 m2 and 30 m2, and the actual midpoint sectional area is 18 m2. By how much does the TRAPEZOIDAL volume exceed the PRISMOIDAL volume?

A 20 m3. B 30 m3. C 40 m3. D 60 m3.

Question 19 ప్రశ్న 19

Consider the following statements about the trapezoidal method of earthwork computation. Statement I: The method gives the exact geometric volume when cross-sectional area varies linearly with longitudinal distance. Statement II: If the actual midpoint area equals the arithmetic mean of the two end areas, the trapezoidal and prismoidal formulas give identical volumes. Which option is correct?

A Statement I only. B Statement II only. C Neither Statement I nor Statement II. D Both Statement I and Statement II.

Question 20 ప్రశ్న 20

A symmetrical embankment has a formation width of 10 m and side slopes of 2 horizontal to 1 vertical on level transverse ground. The end filling depths are 0.5 m and 1.5 m over a 20 m interval. By how much does the TRAPEZOIDAL volume exceed the MID-SECTIONAL volume when the midpoint depth is taken as the mean of the end depths?

A 10 m3. B 5 m3. C 15 m3. D 20 m3.

Question 21 ప్రశ్న 21

Five consecutive earthwork cross sections have areas of 6 m2, 10 m2, 14 m2, 10 m2 and 6 m2. All four longitudinal intervals are 20 m. Which total volume is obtained using the composite trapezoidal rule?

A 760 m3. B 800 m3. C 820 m3. D 840 m3.

Question 22 ప్రశ్న 22

Four consecutive earthwork sections have areas of 8 m2, 12 m2, 20 m2 and 28 m2 at equal 10 m intervals. An estimator incorrectly takes the simple mean of ALL FOUR areas and multiplies it by the total 30 m length. How does this result compare with the correct composite trapezoidal volume?

A The incorrect method underestimates the volume by 10 m3. B Both procedures give exactly the same volume. C The incorrect method overestimates the volume by 10 m3. D The incorrect method overestimates the volume by 20 m3.

Question 23 ప్రశ్న 23

Four successive earthwork cross sections have areas of 5 m2, 9 m2, 15 m2 and 21 m2. Their respective longitudinal intervals are 10 m, 20 m and 30 m. What is the total volume by the trapezoidal method?

A 800 m3. B 820 m3. C 840 m3. D 850 m3.

Question 24 ప్రశ్న 24

A vertical-sided excavation strip has a constant width of 6 m and a horizontal formation level of RL 100.00 m. At five consecutive stations spaced 20 m apart, the existing ground levels are RL 101.00 m, RL 101.50 m, RL 102.00 m, RL 101.00 m and RL 100.50 m. What is the total cutting volume by the composite trapezoidal method?

A 630 m3. B 600 m3. C 660 m3. D 690 m3.

Question 25 ప్రశ్న 25

A road earthwork alignment has six successive cross sections. Their data, in order, are: cutting area 12 m2 at chainage 0+000; cutting area 18 m2 at 0+020; cutting area 8 m2 at 0+050; zero earthwork area at 0+070; filling area 10 m2 at 0+100; and filling area 20 m2 at 0+130. Assuming linear variation of sectional area within each interval and using the trapezoidal method separately for cutting and filling, what are the TOTAL cutting and filling volumes?

A 770 m3 cutting and 450 m3 filling. B 770 m3 cutting and 600 m3 filling. C 690 m3 cutting and 600 m3 filling. D 850 m3 cutting and 750 m3 filling.

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