---
title: "Aggregate reserve: sandstone 300 m, 227 km2"
subject: "Engineering Geology II"
chapter: 7
key: "semester_4/engineering_geology_ii:reserve-sandstone-227-km2"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-sandstone-227-km2
site: BCT Engineering
---

# Aggregate reserve: sandstone 300 m, 227 km2

Engineering Geology II · Chapter 7: Geology and Construction Materials

- Asked in: 2079 Asoj, 2 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-sandstone-227-km2
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-7

## Question

Calculate the reserve for aggregate of sandstone bedrock having vertical thickness 300 m at S72°W/43° and in an area of 227 km².

## Short answer

True thickness t = 300 cos43° ≈ 219.4 m. Volume = 227 km² × 0.2194 km = 49.8 km³ (4.98×10¹⁰ m³).

## Answer

**Principle:** reserve (volume) of a bed = area $\times$ true thickness, where the true thickness is obtained from the vertical thickness by $t = t_v\cos\delta$.

#### Given
Vertical thickness $t_v = 300$ m, attitude S72°W/43° (dip $\delta = 43^\circ$), area $A = 227\ \text{km}^2$.

#### Calculation
$$
\begin{aligned}
t &= 300\cos 43^\circ = 300 \times 0.7314 = 219.41\ \text{m} = 0.2194\ \text{km} \\
V &= A \times t = 227 \times 0.2194 = 49.81\ \text{km}^3
\end{aligned}
$$
$$
V = 49.81\ \text{km}^3 = 4.98 \times 10^{10}\ \text{m}^3
$$

**Answer: reserve of sandstone aggregate = 49.8 km³ (4.98 × 10¹⁰ m³).**

(If the 227 km² is the plan area on the map, the volume under it is $A\times t_v = 227 \times 0.3 = 68.1\ \text{km}^3$.)

## Check yourself

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

1. How is reserve found from vertical thickness and area?
   A. Multiply area by tv sin δ
   B. Divide area by tv
   C. Multiply area by dip direction
   D. Convert to true thickness t = tv cos δ and multiply by area
   Answer: D. Volume = area x true thickness. (Key point: Formula)

2. What is the true thickness for tv = 300 m and dip 43°?
   A. About 204.6 m
   B. About 219.4 m
   C. About 410.1 m
   D. About 300 m
   Answer: B. 300 x cos 43° = 300 x 0.7314 = 219.4 m. (Key point: True thickness)

3. What volume results for 227 km²?
   A. About 68.1 km³
   B. About 227 km³
   C. About 0.0498 km³
   D. About 49.8 km³ (4.98 x 10^10 m³)
   Answer: D. 227 x 0.2194 = 49.8 km³; 68.1 km³ would use tv instead of true thickness. (Key point: Volume)

## Close variants set in other exams

- [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×

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