---
title: "Numerical: 32-cell system area and channels"
subject: "Wireless Communication"
chapter: 2
key: "semester_7/wireless_communication:cellular-32-cells-capacity"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/cellular-32-cells-capacity
site: BCT Engineering
---

# Numerical: 32-cell system area and channels

Wireless Communication · Chapter 2: Cellular Mobile Communication Concepts

- Asked in: 2082 Bhadra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/cellular-32-cells-capacity
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-2

## Question

The cellular system has 32 cells, each cell has a 1.6 km radius and the system reuse factor is 7. The system is to support 336 traffic channels in total. Determine the total geographical area covered, the number of traffic channels per cell and the total number of simultaneous calls supported by this system.

## Short answer

Each hexagonal cell has area 6.651 km², so total area is 212.8 km². With reuse factor 7 and 336 channels, each cell gets 48 channels, supporting 1536 simultaneous calls.

## Answer

**Given:** number of cells = 32, R = 1.6 km, N = 7, total traffic channels S = 336.

**Area of one hexagonal cell:**
```text
A_cell = (3√3/2) R² = 2.598 × 1.6² = 2.598 × 2.56
       = 6.651 km²
```

**Total area covered:**
```text
A_total = 32 × 6.651 = 212.83 km²
```

**Traffic channels per cell:**
```text
k = S / N = 336 / 7 = 48 channels per cell
```

**Total simultaneous calls:**
```text
C = 48 × 32 = 1536 calls
```
(Number of clusters = 32/7 ≈ 4.57, and C = M × S gives the same value 4.57 × 336 = 1536.)

**Answer: Area ≈ 212.8 km², 48 channels per cell, 1536 simultaneous calls.**

## Check yourself

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

1. Area of a hexagonal cell of radius R is:
   A. 2.598 R^2
   B. 3.14 R^2
   C. R^2
   D. 6 R^2
   Answer: A. A = (3 sqrt3/2) R^2 = 2.598 R^2, i.e. 6.651 km2 for R = 1.6 km. (Key point: Cell area)

2. Total area covered by 32 cells is about:
   A. 6.65 km2
   B. 212.8 km2
   C. 48 km2
   D. 51.2 km2
   Answer: B. 32 x 6.651 = 212.83 km2. (Key point: Total area)

3. Channels per cell with 336 channels and N = 7:
   A. 48
   B. 336
   C. 7
   D. 32
   Answer: A. k = 336/7 = 48. (Key point: Channels per cell)

4. Total simultaneous calls:
   A. 48 x 32 = 1536
   B. 336
   C. 48 x 7 = 336
   D. 32 x 7 = 224
   Answer: A. Each of 32 cells supports 48 calls. (Key point: Simultaneous calls)

## Related in Wireless Communication

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- [Numerical: cellular vs non-cellular voice channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-vs-noncellular-channels) — Wireless Communication, chapter 2
- [Numerical: 12-cell system capacity at 2% GOS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-capacity-12-cell-system) — Wireless Communication, chapter 2
- [Numerical: co-channel distance for 7-cell reuse](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acochannel-distance-seven-cell) — Wireless Communication, chapter 2
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- [Numerical: maximum cell radius using Hata model](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ahata-max-cell-radius) — Wireless Communication, chapter 3

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