---
title: "Sampler clearances and area ratio (59 mm)"
subject: "Foundation Engineering"
chapter: 2
key: "semester_5/foundation_engineering:sampler-clearance-59-63"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-clearance-59-63
site: BCT Engineering
---

# Sampler clearances and area ratio (59 mm)

Foundation Engineering · Chapter 2: Soil Exploration

- Asked in: 2081 Baisakh, 3 marks
- Video: [soil sampler | Area Ratio | Recovery Ratio | Inside clearance | outside clearance | Foundation](https://www.youtube.com/watch?v=oreHo3XXhkU) — Sudip Dhakal
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-clearance-59-63
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-2

## Question

A sampler has the following dimensions: inside diameter of cutting edge = 59 mm; outside diameter of cutting edge = 63 mm; inside diameter of sampling tube = 60 mm and outside diameter of sampling tube = 62 mm. Calculate (i) area ratio (ii) inside clearance (iii) outside clearance.

## Short answer

Inside clearance Ci=1.69%, outside clearance Co=1.61%, area ratio Ar=14.02%. Clearances acceptable but Ar > 10% indicates slight disturbance.

## Answer

Given: $D_1 = 59$ mm (cutting edge inside), $D_3 = 63$ mm (cutting edge outside), $D_2 = 60$ mm (tube inside), $D_4 = 62$ mm (tube outside).

**(i) Area ratio**
$$
A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100 = \frac{63^2-59^2}{59^2}\times100 = \frac{488}{3481}\times100 = 14.02\%
$$

**(ii) Inside clearance**
$$
C_i = \frac{D_2-D_1}{D_1}\times100 = \frac{60-59}{59}\times100 = 1.69\%
$$

**(iii) Outside clearance**
$$
C_o = \frac{D_3-D_4}{D_4}\times100 = \frac{63-62}{62}\times100 = 1.61\%
$$

**Answer:** $A_r = 14.02\%$, $C_i = 1.69\%$, $C_o = 1.61\%$. (The clearances are acceptable, but $A_r > 10\%$, so the sample would be slightly disturbed.)

## Check yourself

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

1. With D1 = 59 and D3 = 63 mm, the area ratio is
   A. 6.78%
   B. 14.02%
   C. 1.69%
   D. 7.1%
   Answer: B. (63^2 - 59^2)/59^2 = 488/3481. (Key point: Area ratio)

2. With D1 = 59 and D2 = 60 mm, the inside clearance is
   A. 1.61%
   B. 1.69%
   C. 14.02%
   D. 1.0%
   Answer: B. (60 - 59)/59 x 100. (Key point: Inside clearance)

3. With D3 = 63 and D4 = 62 mm, the outside clearance is
   A. 1.69%
   B. 1.61%
   C. 1.59%
   D. 3.2%
   Answer: B. (63 - 62)/62 x 100; divided by D4 not D3. (Key point: Outside clearance)

## Close variants set in other exams

- [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×

## 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
- [Area ratio of sampler, radius 30 mm](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-area-ratio-radius) — Foundation Engineering, chapter 2