---
title: "Sand deposit reserve in tons"
subject: "Engineering Geology II"
chapter: 7
key: "semester_4/engineering_geology_ii:reserve-sand-deposit-tons"
source: https://www.bctengineer.com/q/semester_4/engineering_geology_ii/reserve-sand-deposit-tons
site: BCT Engineering
---

# Sand deposit reserve in tons

Engineering Geology II · Chapter 7: Geology and Construction Materials

- Asked in: 2076 Bhadra, 2.5 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-sand-deposit-tons
- Whole chapter: https://www.bctengineer.com/md/semester_4/engineering_geology_ii/chapter-7

## Question

A 16 m thick sand deposit extends horizontally within the terrace which is covered by 150 m × 150 m with density 2870 kg/m³. Estimate the reserve of sand deposit in tons.

## Short answer

For a horizontal sand deposit, reserve volume = area × thickness = 22,500 m² × 16 m = 360,000 m³. Mass = volume × density 2870 kg/m³ = 1.033×10⁹ kg (1,033,200 tonnes).

## Answer

**Principle:** for a horizontal deposit the thickness is the true thickness, so reserve (volume) = area $\times$ thickness; mass = volume $\times$ density.

#### Given
Thickness $t = 16$ m; area $= 150 \times 150 = 22{,}500\ \text{m}^2$; density $\rho = 2870\ \text{kg/m}^3$.

#### Calculation
$$
\begin{aligned}
V &= 22{,}500 \times 16 = 360{,}000\ \text{m}^3 \\
M &= V\rho = 360{,}000 \times 2870 = 1.0332\times 10^{9}\ \text{kg} \\
&= 1{,}033{,}200\ \text{tonnes}
\end{aligned}
$$
(1 tonne = 1000 kg.)

**Answer: reserve of sand = 3.6 × 10⁵ m³, i.e. about 1.03 × 10⁶ tonnes (1,033,200 t).**

## Check yourself

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

1. Why is no cos δ correction needed here?
   A. Sand has no dip direction
   B. Dip is always 90° for sand
   C. Density replaces the correction
   D. The deposit is horizontal, so its thickness is the true thickness
   Answer: D. With zero dip, cos 0° = 1. (Key point: Horizontal deposit)

2. What volume does the deposit hold?
   A. 22,500 m³
   B. 360,000 m³
   C. 3,600,000 m³
   D. 1,033,200 m³
   Answer: B. 150 x 150 x 16 = 360,000 m³. (Key point: Volume)

3. How is tonnage found?
   A. Volume / density = 125 m³
   B. Volume x density = 1.03 x 10^9 tonnes
   C. Area x density = 6.5 x 10^7 kg
   D. Volume x density = 1.0332 x 10^9 kg = about 1.03 million tonnes
   Answer: D. 360,000 x 2870 = 1.0332 x 10^9 kg; dividing by 1000 gives tonnes. (Key point: Mass)

## Related in Engineering Geology II

- [Define reserve and estimate construction material](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Adefine-reserve-estimation) — Engineering Geology II, chapter 7, asked 10×
- [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

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