---
title: "Sampler clearances and area ratio (69 mm)"
subject: "Foundation Engineering"
chapter: 2
key: "semester_5/foundation_engineering:sampler-clearance-69-73"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-clearance-69-73
site: BCT Engineering
---

# Sampler clearances and area ratio (69 mm)

Foundation Engineering · Chapter 2: Soil Exploration

- Asked in: 2076 Asoj, 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-69-73
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-2

## Question

A soil sampler has the following dimensions: inside diameter of the cutting edge = 69 mm; outside diameter of cutting edge = 73 mm; inside diameter of the sampling tube = 70 mm and outside diameter of the sampling tube = 72 mm. Calculate: (i) inside clearance (ii) outside clearance and (iii) area ratio of the sampler.

## Short answer

Inside clearance Ci=1.45%, outside clearance Co=1.39%, area ratio Ar=11.93%. Clearances are within limits, but Ar is marginally above 10%.

## Answer

Given: $D_1 = 69$ mm, $D_3 = 73$ mm (cutting edge inside/outside), $D_2 = 70$ mm, $D_4 = 72$ mm (tube inside/outside).

**(i) Inside clearance**
$$
C_i = \frac{D_2-D_1}{D_1}\times100 = \frac{70-69}{69}\times100 = 1.45\%
$$

**(ii) Outside clearance**
$$
C_o = \frac{D_3-D_4}{D_4}\times100 = \frac{73-72}{72}\times100 = 1.39\%
$$

**(iii) Area ratio**
$$
A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100 = \frac{73^2-69^2}{69^2}\times100 = \frac{568}{4761}\times100 = 11.93\%
$$

**Answer:** $C_i = 1.45\%$, $C_o = 1.39\%$, $A_r = 11.93\%$. Both clearances are within limits; the area ratio is a little over the 10% limit for a good undisturbed sample.

## Check yourself

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

1. With D1 = 69 and D2 = 70 mm, inside clearance is
   A. 1.39%
   B. 11.93%
   C. 1.0%
   D. 1.45%
   Answer: D. (70 - 69)/69 x 100. (Key point: Inside clearance)

2. With D3 = 73 and D4 = 72 mm, outside clearance is
   A. 1.45%
   B. 1.37%
   C. 2.8%
   D. 1.39%
   Answer: D. (73 - 72)/72 x 100. (Key point: Outside clearance)

3. The area ratio is
   A. 1.45%
   B. 11.93%
   C. 5.9%
   D. 8.0%
   Answer: B. (73^2 - 69^2)/69^2 = 568/4761; slightly over 10%. (Key point: Area ratio)

## Close variants set in other exams

- [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×

## 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