---
title: "Aggregate reserve: quartzite 300 m, 437 km2"
subject: "Engineering Geology II"
chapter: 7
key: "semester_4/engineering_geology_ii:reserve-quartzite-437-km2"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-quartzite-437-km2
site: BCT Engineering
---

# Aggregate reserve: quartzite 300 m, 437 km2

Engineering Geology II · Chapter 7: Geology and Construction Materials

- Asked in: 2073 Bhadra, 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-437-km2
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-7

## Question

Calculate the reserve for aggregate of quartzite bedrock having vertical thickness 300 m at S72°W/43° and in an area of 437 km².

## Short answer

True thickness t = 300 cos43° = 219.4 m. Volume = 437 km² × 0.2194 km = 95.9 km³ (9.59×10¹⁰ m³).

## Answer

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

#### Given
$t_v = 300$ m, attitude S72°W/43° (dip $43^\circ$), area $A = 437\ \text{km}^2$.

#### Calculation
$$
\begin{aligned}
t &= 300\cos 43^\circ = 219.41\ \text{m} = 0.2194\ \text{km} \\
V &= 437 \times 0.2194 = 95.88\ \text{km}^3 = 9.59 \times 10^{10}\ \text{m}^3
\end{aligned}
$$

**Answer: reserve of quartzite aggregate = 95.9 km³ (9.59 × 10¹⁰ m³).**

(If 437 km² is the plan area, the volume under it is $437 \times 0.3 = 131.1\ \text{km}^3$.)

## Check yourself

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

1. Which attitude data is needed for the thickness correction?
   A. Only the strike S72°W
   B. The dip direction and strike but not dip amount
   C. Neither; thickness needs no correction
   D. Only the dip amount (43°)
   Answer: D. t = tv cos δ uses the dip amount alone. (Key point: Dip needed)

2. What is the true thickness?
   A. About 300 m
   B. About 219.4 m
   C. About 204.6 m
   D. About 410 m
   Answer: B. 300 cos 43° = 219.4 m. (Key point: True thickness)

3. What is the reserve for 437 km²?
   A. About 131.1 km³
   B. About 437 km³
   C. About 59.6 km³
   D. About 95.9 km³
   Answer: D. 437 x 0.2194 = 95.9 km³; 131.1 km³ uses tv. (Key point: Volume)

## Close variants set in other exams

- [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×

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