---
title: "Reserve: quartzite 400 m, 537 km2"
subject: "Engineering Geology II"
chapter: 7
key: "semester_4/engineering_geology_ii:reserve-quartzite-537-km2"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-quartzite-537-km2
site: BCT Engineering
---

# Reserve: quartzite 400 m, 537 km2

Engineering Geology II · Chapter 7: Geology and Construction Materials

- Asked in: 2078 Baisakh, 3 marks
- 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-quartzite-537-km2
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-7

## Question

Calculate the reserve for construction of quartzite bed having vertical thickness 400 m at S72°W/48°SE in an area of 537 km².

## Short answer

True thickness = 400 cos48° = 267.65 m = 0.2677 km. Reserve = area × true thickness = 537 km² × 0.2677 km = 143.7 km³ (1.44×10¹¹ m³).

## Answer

**Principle:** reserve = area $\times$ true thickness, with $t = t_v\cos\delta$.

#### Given
$t_v = 400$ m, attitude S72°W/48° SE (dip $\delta = 48^\circ$), area $A = 537\ \text{km}^2$.

#### Calculation
$$
\begin{aligned}
t &= 400\cos 48^\circ = 400 \times 0.6691 = 267.65\ \text{m} = 0.2677\ \text{km} \\
V &= 537 \times 0.2677 = 143.73\ \text{km}^3 = 1.44 \times 10^{11}\ \text{m}^3
\end{aligned}
$$

**Answer: reserve of quartzite = 143.7 km³ (1.44 × 10¹¹ m³).**

(If 537 km² is the plan area, the volume under it is $537 \times 0.4 = 214.8\ \text{km}^3$.)

## Check yourself

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

1. What is the true thickness for tv = 400 m, dip 48°?
   A. About 297.3 m
   B. About 400 m
   C. About 597.8 m
   D. About 267.7 m
   Answer: D. 400 x 0.6691 = 267.65 m. (Key point: True thickness)

2. What is the reserve for 537 km²?
   A. About 214.8 km³
   B. About 143.7 km³
   C. About 537 km³
   D. About 1.44 km³
   Answer: B. 537 x 0.2677 = 143.7 km³. (Key point: Reserve)

3. If 537 km² were the plan area, what would the volume be?
   A. Area x true thickness = 143.7 km³
   B. Area x tv x cos δ x cos δ
   C. Area x tan δ
   D. Area x tv = 214.8 km³
   Answer: D. Under a plan area the vertical thickness applies, giving 537 x 0.4 = 214.8 km³. (Key point: Plan area case)

## Related in Engineering Geology II

- [Aggregate reserve: quartzite 300 m, 437 km2](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-quartzite-437-km2) — Engineering Geology II, chapter 7, asked 2×
- [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×
- [Aggregate reserve: sandstone 300 m, 227 km2](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-sandstone-227-km2) — Engineering Geology II, chapter 7, asked 2×
- [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 quartzite bed dipping S25°E](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-quartzite-bed-dipping) — Engineering Geology I, chapter 5, asked 2×
- [Strike of quartzite bed towards S20°W](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-quartzite-bed-towards) — Engineering Geology I, chapter 5
- [Strike of quartzite bed, dip 70° towards S20°E](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-quartzite-bed-dip) — Engineering Geology I, chapter 5
- [Strike of quartzite bed, dip 80° towards N10°E](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-quartzite-bed-dip-80) — Engineering Geology I, chapter 5