---
title: "Area ratio of sampler, radius 30 mm"
subject: "Foundation Engineering"
chapter: 2
key: "semester_5/foundation_engineering:sampler-area-ratio-radius"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-area-ratio-radius
site: BCT Engineering
---

# Area ratio of sampler, radius 30 mm

Foundation Engineering · Chapter 2: Soil Exploration

- Asked in: 2074 Chaitra, 2+1 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-area-ratio-radius
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-2

## Question

Determine the area ratio of a sampler having an external radius of 30 mm and a wall thickness of 2.25 mm. Do you recommend this sampler for obtaining undisturbed soil samples and why?

## Short answer

Inside diameter D1=60−2×2.25=55.5 mm, Ar=(60²−55.5²)/55.5²×100=16.87%. Not recommended for undisturbed sampling because Ar >> 10%, causing excessive soil displacement.

## Answer

External radius 30 mm gives outside diameter $D_3 = 60$ mm. Wall thickness 2.25 mm gives inside diameter
$$
D_1 = 60 - 2\times2.25 = 55.5\ \text{mm}
$$

$$
A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100 = \frac{60^2-55.5^2}{55.5^2}\times100 = \frac{519.75}{3080.25}\times100 = 16.87\%
$$

**Answer:** $A_r = 16.87\%$.

**Recommendation:** not recommended for undisturbed sampling. The area ratio is more than 10% (limit 10%, or 20% at most for stiff soil), so the thick wall displaces too much soil and disturbs the sample. It is fit only for disturbed or stiff-soil sampling.

## Check yourself

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

1. With external radius 30 mm and wall thickness 2.25 mm, D1 is
   A. 55.5 mm
   B. 57.75 mm
   C. 60 mm
   D. 52.5 mm
   Answer: A. D3 = 60; D1 = 60 - 2 x 2.25 = 55.5. (Key point: Inside diameter)

2. The area ratio is
   A. 16.87%
   B. 8.1%
   C. 4.5%
   D. 10.0%
   Answer: A. (60^2 - 55.5^2)/55.5^2 = 519.75/3080.25. (Key point: Area ratio)

3. The sampler is
   A. not recommended for undisturbed sampling since Ar > 10%
   B. recommended since Ar < 20%
   C. recommended always
   D. recommended for soft clay
   Answer: A. Thick wall displaces too much soil. (Key point: Recommendation)

## Related in Foundation Engineering

- [Sampler clearances and area ratio (68 mm)](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-clearance-68-70) — Foundation Engineering, chapter 2
- [Sampler clearances and area ratio (69 mm)](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-clearance-69-73) — Foundation Engineering, chapter 2, asked 2×
- [Sampler clearances and area ratio (59 mm)](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-clearance-59-63) — Foundation Engineering, chapter 2, asked 2×
- [Sampler disturbed or undisturbed check](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-40-42-mm) — Foundation Engineering, chapter 2
- [Disturbed vs undisturbed samples](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Adisturbed-vs-undisturbed-sample) — Foundation Engineering, chapter 2, asked 2×
- [Why undisturbed samples are required](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awhy-undisturbed-samples) — Foundation Engineering, chapter 2

## Related in other subjects

- [Settling tank 30 m x 3 m, 0.02 mm at 25°C; 0.01 mm at 10°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-as70) — Water Supply Engineering, chapter 6, asked 3×
- [Settling tank 30 m x 3 m, 0.03 mm at 25°C; 0.025 mm at 20°C](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ased-k72) — Water Supply Engineering, chapter 6, asked 3×
- [Single-storey external wall: stress, brick, mortar](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Awall-single-storey-100kn-12mm) — Concrete Technology and Masonry Structure, chapter 8
- [Furnace wall: insulation thickness for heat loss](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Afurnace-fireclay-insulation-thickness) — Fundamental of Thermodynamics & Heat Transfer, chapter 7