The radius of a cylinder with a diameter of 18 cm is 9 cm.
Understanding the fundamental relationship between a circle's diameter and its radius is key to solving this and many other geometry problems. This relationship applies universally to any circular object, including the circular bases of a cylinder.
Understanding Radius and Diameter
To accurately determine the radius from a given diameter, it's essential to grasp what each term represents:
- Radius (r): The distance from the exact center of a circle to any point on its circumference (the edge). Think of it as half the width of the circle. You can learn more about the definition of radius from credible sources like Khan Academy.
- Diameter (d): The distance across a circle, passing through its center. It is essentially the widest part of the circle. The diameter is always twice the length of the radius.
The Relationship Between Radius and Diameter
The relationship is straightforward and can be expressed with simple formulas:
- Diameter = 2 × Radius
- Radius = Diameter / 2
In the context of a cylinder, the base is a circle. Therefore, its radius and diameter follow these same rules. When a cylinder has a diameter of 18 cm, its radius is simply half of that value.
Calculating the Radius
Given the diameter of the cylinder is 18 cm, we can use the formula:
- Identify the given value: Diameter (d) = 18 cm.
- Apply the formula: Radius (r) = Diameter / 2.
- Perform the calculation: r = 18 cm / 2 = 9 cm.
Thus, the radius of the cylinder is 9 cm.
Practical Insights
Knowing the radius of a cylinder is crucial for various calculations and real-world applications, such as:
- Volume Calculation: The volume of a cylinder is calculated using the formula
V = πr²h, whereris the radius andhis the height. Without the radius, calculating the volume would be impossible. - Surface Area Calculation: To determine the surface area of a cylinder (
A = 2πrh + 2πr²), the radius is a fundamental component. - Engineering and Design: Engineers often need to specify the radius for components like pipes, tubes, or shafts to ensure they fit correctly or have the desired capacity.
- Manufacturing: Precision in radius measurement is vital in manufacturing industries for creating parts that meet exact specifications.
Summary of Measurements
Here's a quick overview of the measurements for this specific cylinder:
| Measurement | Value |
|---|---|
| Diameter | 18 cm |
| Radius | 9 cm |
Key Takeaways
- The radius is always half of the diameter.
- Understanding this basic geometric relationship is fundamental for solving more complex problems involving circles and cylinders.
- The radius is a critical parameter for calculating volume, surface area, and for practical design and engineering applications.
