---
title: "Road earthwork, upward grade 1:100"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:road-earthwork-u-upward-1-100"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/road-earthwork-u-upward-1-100
site: BCT Engineering
---

# Road earthwork, upward grade 1:100

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2066 Bhadra (old course), 5 marks
- Video: [Estimation of Road (Numerical-3)|| Roadwork Qnty Estimation || Lecture 30 || QSC || Aditya Agrawal](https://www.youtube.com/watch?v=pm3erfgjQaY) — Aditya Agrawal: A Civil Engineer
- 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-u-upward-1-100
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Estimate the quantity of earth work for a portion of road, when formation width is 10 m. Side slope in cutting and filling are 1:1 and 2:1 respectively.

| Distance | 0 m | 30 m | 60 m | 90 m |
|---|---|---|---|---|
| R.L.G | 100 m | 110 m | 111 m | 112 m |
| R.L.F | 100 m, upward grade (1:100) | | | |
(as printed; the ground level row is hard to read)

## Short answer

Earthwork in cutting = 15,610.65 m³; earthwork in filling = 0.00 m³.

## Answer

#### Given data and assumptions
- Formation width $B = 10$ m; side slopes: cutting $1:1$, filling $2:1$. Ground is level across the road.
- Ground levels are read as printed (100, 110, 111, 112 m at 0, 30, 60, 90 m, the scan is hard to read) and formation level starts at 100.00 m, rising 1 in 100.

#### 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+000 | 100.000 | 100.000 | 0.000 |
| 0+030 | 110.000 | 100.300 | cutting 9.700 |
| 0+060 | 111.000 | 100.600 | cutting 10.400 |
| 0+090 | 112.000 | 100.900 | cutting 11.100 |

#### Sectional areas
| Chainage | Centre ht. $h$ (m) | Cutting area (m²) | Filling area (m²) |
|---|---:|---:|---:|
| 0+000 | 0.00 | 0.000 | 0.000 |
| 0+030 | cut 9.70 | 191.090 | 0.000 |
| 0+060 | cut 10.40 | 212.160 | 0.000 |
| 0+090 | cut 11.10 | 234.210 | 0.000 |

#### Volumes
| Between | Distance (m) | Cutting (m³) | Filling (m³) |
|---|---:|---:|---:|
| 0+000 – 0+030 | 30.0 | 2,866.35 | 0.00 |
| 0+030 – 0+060 | 30.0 | 6,048.75 | 0.00 |
| 0+060 – 0+090 | 30.0 | 6,695.55 | 0.00 |
| **Total** | 90.0 | **15,610.65** | **0.00** |

**Answer: Earthwork in cutting = 15,610.65 m³; earthwork in filling = 0.00 m³.**

## Check yourself

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

1. Formation starts at 100.00 m at 0 m and rises 1 in 100. What is the formation level at 30 m?
   A. 100.10 m
   B. 100.30 m
   C. 103.00 m
   D. 99.70 m
   Answer: B. Rise = 30/100 = 0.30 m, so level is 100.30 m. (Key point: Formation level)

2. At 30 m the ground is 110.00 m and formation 100.30 m (cutting 9.70 m, slope 1:1, B = 10 m). The area is:
   A. 97.0 m^2
   B. 191.09 m^2
   C. 382.18 m^2
   D. 48.5 m^2
   Answer: B. A = (10 + 1 x 9.70) x 9.70 = 191.09 m^2. (Key point: Cutting depth and area)

3. Why is the filling volume zero in this problem?
   A. Side slope in filling is zero
   B. Ground is at or above formation level at all sections
   C. Formation width is too small
   D. Mean area method gives no filling
   Answer: B. Ground rises faster than the formation, so every section is in cutting (zero at 0 m). (Key point: Why no filling)

## Related in Estimating and Costing

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## Related in other subjects

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- [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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- [Cutting volume, 60 m, GL 540.70, formation 538.20](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Avolume-cutting-60m-gl-540-70) — Surveying I, chapter 9, asked 7×