---
title: "Reserve: limestone dip 30, apparent 20 m"
subject: "Engineering Geology II"
chapter: 7
key: "semester_4/engineering_geology_ii:reserve-limestone-dip-30"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-limestone-dip-30
site: BCT Engineering
---

# Reserve: limestone dip 30, apparent 20 m

Engineering Geology II · Chapter 7: Geology and Construction Materials

- Asked in: 2077 Chaitra, 2 marks
- Video: [1 Thickness Problems_Engineering Geology (VTU SVIT SAVI)](https://www.youtube.com/watch?v=5KdMJOwHRc0) — Sai Vidya Institute of Technology - SVIT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-limestone-dip-30
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-7

## Question

Calculate the reserve for limestone bed having dip amount 30°, apparent thickness of 20 m in 1128.5 m² area.

## Short answer

True thickness = apparent thickness × cos30° = 20×0.866 = 17.32 m. Reserve = 1128.5 m² × 17.32 m = 19,546 m³ (1.95×10⁴ m³).

## Answer

**Principle:** the apparent (vertical) thickness measured in a borehole is converted to true thickness by $t = t_v\cos\delta$; reserve = area $\times$ true thickness.

#### Given
Dip $\delta = 30^\circ$, apparent thickness $t_v = 20$ m, area $A = 1128.5\ \text{m}^2$.

#### Calculation
$$
\begin{aligned}
t &= 20\cos 30^\circ = 20 \times 0.8660 = 17.32\ \text{m} \\
V &= 1128.5 \times 17.32 = 19{,}546\ \text{m}^3
\end{aligned}
$$

**Answer: reserve of limestone = 19,546 m³ (about 1.95 × 10⁴ m³).**

(If the area is the plan area, the volume is $1128.5 \times 20 = 22{,}570\ \text{m}^3$.)

## Check yourself

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

1. What is 'apparent thickness' here?
   A. The thickness measured perpendicular to bedding
   B. The thickness along strike
   C. The vertical thickness measured in a borehole, which exceeds true thickness
   D. The thickness of overburden
   Answer: C. Apparent thickness is converted by t = tv cos δ. (Key point: Apparent thickness)

2. What is the true thickness for tv = 20 m, dip 30°?
   A. About 17.3 m
   B. About 10 m
   C. About 23.1 m
   D. About 20 m
   Answer: A. 20 x 0.866 = 17.32 m. (Key point: True thickness)

3. What volume results for 1128.5 m²?
   A. About 22,570 m³
   B. About 11,285 m³
   C. About 19,546 m³
   D. About 39,100 m³
   Answer: C. 1128.5 x 17.32 = 19,546 m³; 22,570 would use tv. (Key point: Reserve)

## Related in Engineering Geology II

- [Limestone reserve for cement factory](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-limestone-cement-density) — Engineering Geology II, chapter 7
- [Reserve: quartzite apparent dips 1:9 and 1:12, 4.6 km2](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-quartzite-apparent-dips-area) — Engineering Geology II, chapter 7, asked 2×
- [Reserve: quartzite apparent dips 1:9 and 1:12, 2.7 x 3.1 km](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-quartzite-apparent-dips-terrain) — Engineering Geology II, chapter 7, asked 2×
- [True dip from two apparent dips](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atrue-dip-from-apparent-dips) — Engineering Geology II, chapter 6
- [True thickness: limestone vertical 600 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atrue-thickness-limestone-600m) — Engineering Geology II, chapter 7
- [Limestone true thickness: A 600 m N28E, C 400 m S10W](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-limestone-true-thickness-a600) — Engineering Geology II, chapter 6, asked 2×

## Related in other subjects

- [Strike of limestone bed, dip N40°W, 64°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bed-dip) — Engineering Geology I, chapter 5
- [Strike of limestone bed directed N20°E, dip 45°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bed-directed) — Engineering Geology I, chapter 5
- [Calculating apparent dip from true dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Acalculating-apparent-dip-from-true) — Engineering Geology I, chapter 5, asked 2×
- [Strike-dip relationship and apparent dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrikedip-relationship-and-apparent-dip) — Engineering Geology I, chapter 5, asked 2×