Introduction

Understanding the relationship between the circumference and diameter of a cylinder is crucial in many practical applications, such as determining how many times a thread can be wound around a cylinder. In this article, we'll explore the math behind this calculation and provide a step-by-step guide to solving similar problems.

Calculating the Circumference

The formula to calculate the circumference (C) of a circle (or cylinder) given its diameter (d) is:

C πd

Where π (pi) is approximately 3.14159.

Step-by-Step Calculation

Given a cylinder with a diameter of 4.2 cm, we first calculate the circumference:

C πd

C 3.14159 × 4.2 cm ≈ 13.188 cm

Now, we need to determine how many times a 132-cm thread can be wound around the cylinder. To do this, we use the formula:

Number of rounds Length of thread / Circumference of cylinder

Number of rounds 132 cm / 13.188 cm ≈ 10.079 rounds

Simplifying the Process

For simplicity, we can approximate π to 22/7, which gives us a more precise manual calculation:

C (22/7) × 4.2 cm ≈ 13.2 cm

Number of rounds 132 cm / 13.2 cm 10 rounds

Revisiting the Calculation

Alternatively, we can break down the calculation by considering 1 cm of thread making 1/132 rounds. Therefore, 132 cm of thread will make:

Number of rounds 132 × (1/132) 10 rounds

Summary

In conclusion, a 132 cm thread can be wound around a cylinder with a diameter of 4.2 cm approximately 10 times. This result is consistent across the different calculation methods, confirming the accuracy of the solution.

Knowing how to perform such calculations is essential in various fields, including engineering, manufacturing, and design. Understanding the relationship between circumference and diameter helps in optimizing materials usage and improving overall productivity.