---
title: "Road earthwork, formation level at 150 m"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:road-earthwork-t-grade-150"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/road-earthwork-t-grade-150
site: BCT Engineering
---

# Road earthwork, formation level at 150 m

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2067 Poush (old course), 10 marks
- Video: [Calculation of Volume of Earthwork from Cross Sections | Road Estimate | Earthwork Calculation](https://www.youtube.com/watch?v=zMl6OVLeKWM) — Civil Engineering Edu
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/estimating_and_costing/road-earthwork-t-grade-150
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Find out the quantity of earth work of a portion of road to be constructed with the following data: Formation width of the road = 10 m. Side slopes in banking and cutting = (2:1) and (1:1). Downward grade 1 in 120 from distance 90 to 120 m while it remains in level from distance 120 to 180 m and again upward grade 1 in 90 from distance 180 to 210 m. The formation level at distance 150 m = 1197.50.

| R.L. of ground | 1198.65 | 1196.40 | 1199.30 | 1200.40 | 1198.10 |
|---|---|---|---|---|---|
| Distance (m) | 90 | 120 | 150 | 190 | 210 |

## Short answer

Earthwork in cutting = 1,786.15 m³; earthwork in filling = 187.07 m³.

## Answer

#### Given data and assumptions
- Formation width $B = 10$ m; banking slope $2:1$, cutting slope $1:1$. Ground is level across the road. Stations are at 90, 120, 150, 190 and 210 m (spacing 30, 30, 40, 20 m).
- Formation level at 150 m is 1197.50 m; level from 120 m to 180 m; falling 1 in 120 from 90 to 120 m, so level at 90 m = 1197.75 m; rising 1 in 90 from 180 m, so level at 190 m = 1197.50 + 10/90 = 1197.611 m and at 210 m = 1197.833 m.

#### Method
Level (plain-ground) sections are used. With centre height $h$, formation width $B$ and side slope $s:1$:

$$
A = (B + s\,h)\,h
$$

Volume between two sections = mean area × distance; where a section changes from cutting to filling, the length of each part is found by proportion of the depths and the volume of each part = ½ × end area × length.

| Chainage | GL (m) | FL (m) | Depth of cutting / height of filling (m) |
|---|---:|---:|---:|
| 0+090 | 1,198.650 | 1,197.750 | cutting 0.900 |
| 0+120 | 1,196.400 | 1,197.500 | filling 1.100 |
| 0+150 | 1,199.300 | 1,197.500 | cutting 1.800 |
| 0+190 | 1,200.400 | 1,197.611 | cutting 2.789 |
| 0+210 | 1,198.100 | 1,197.833 | cutting 0.267 |

#### Sectional areas
| Chainage | Centre ht. $h$ (m) | Cutting area (m²) | Filling area (m²) |
|---|---:|---:|---:|
| 0+090 | cut 0.90 | 9.810 | 0.000 |
| 0+120 | fill 1.10 | 0.000 | 13.420 |
| 0+150 | cut 1.80 | 21.240 | 0.000 |
| 0+190 | cut 2.79 | 35.667 | 0.000 |
| 0+210 | cut 0.27 | 2.738 | 0.000 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Filling (m³) |
|---|---:|---:|---:|
| 0+090 – 0+120 | 30.0 | 66.22 | 110.71 |
| 0+120 – 0+150 | 30.0 | 197.75 | 76.36 |
| 0+150 – 0+190 | 40.0 | 1,138.14 | 0.00 |
| 0+190 – 0+210 | 20.0 | 384.05 | 0.00 |
| **Total** | 120.0 | **1,786.15** | **187.07** |

**Answer: Earthwork in cutting = 1,786.15 m³; earthwork in filling = 187.07 m³.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Stations are 90, 120, 150, 190, 210 m. What distance applies between the last three sections?
   A. 30 m, 30 m
   B. 40 m then 20 m
   C. 30 m then 40 m
   D. 20 m then 40 m
   Answer: B. 150 to 190 is 40 m and 190 to 210 is 20 m, so volumes use these distances. (Key point: Unequal spacing)

2. The road rises 1 in 90 from 180 m. What is the formation level at 190 m?
   A. 1197.833 m
   B. 1197.500 m
   C. 1197.611 m
   D. 1197.722 m
   Answer: C. Rise over 10 m is 10/90 = 0.111 m, so the level is 1197.50 + 0.111 = 1197.611 m. (Key point: Formation level at 190 m)

3. At 190 m, ground is 1200.40 m and formation 1197.611 m. The cutting depth is about 2.79 m. The area is:
   A. About 27.9 m^2
   B. About 35.7 m^2
   C. About 7.8 m^2
   D. About 55.6 m^2
   Answer: B. A = (B + s h) h = (10 + 2.789) x 2.789 = about 35.67 m^2. (Key point: Cutting depth and area)

4. Cutting areas 21.240 (150 m) and 35.667 (190 m) m^2 give a cutting volume of about:
   A. 1138 m^3
   B. 569 m^3
   C. 853 m^3
   D. 1417 m^3
   Answer: A. Mean area 28.45 m^2 x 40 m = about 1138.14 m^3. (Key point: Volume with longer spacing)

## Close variants set in other exams

- [Road earthwork, grades from 90 m to 210 m (s)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-s-grade-90-210) — Estimating and Costing, chapter 6, asked 3×

## Related in Estimating and Costing

- [Road earthwork, grades 1 in 120 and 1 in 90 (0-120)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-r-grade-120-90) — Estimating and Costing, chapter 6, asked 2×
- [Hill road earthwork, cutting 4 m / banking 6 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-k-cut4-fill6) — Estimating and Costing, chapter 6
- [Road earthwork, RD 0-120, gradient 1 in 150](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-o-rds) — Estimating and Costing, chapter 6
- [Hill road earthwork, 0-90 m (8 m formation)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-p-0-90) — Estimating and Costing, chapter 6
- [Hill road earthwork, 0 m to 90 m, 10/8 m widths](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-e-0-90) — Estimating and Costing, chapter 6, asked 2×
- [Road earthwork, upward grade 1:100](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-u-upward-1-100) — Estimating and Costing, chapter 6

## Related in other subjects

- [Cutting volume, 60 m, formation level 279.00](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-gl-281-50-formation-279) — Surveying I, chapter 9, asked 7×
- [Cutting volume, 60 m, formation level 278.00](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-formation-278-upward) — Surveying I, chapter 9, asked 7×
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