Calculating the Radius of a Circle Given Its Diameter

Understanding the relationship between the diameter and the radius of a circle is a fundamental concept in geometry. This relationship is straightforward and can be applied to solve a variety of problems.

Basic Relationship: Diameter and Radius

The radius of a circle is defined as half of its diameter. This relationship can be expressed mathematically as:

t

Radius Diameter / 2

Given this simple formula, we can easily calculate the radius of a circle if we know its diameter.

Examples

Example 1: Diameter 12 cm

Let's start with a simple problem. If a circle has a diameter of 12 centimeters, we can find its radius by applying the formula provided above.

t tt

Start with the given diameter:

tt

Diameter 12 cm

t t tt

Use the formula to find the radius:

tt

Radius Diameter / 2 12 cm / 2 6 cm

t t tt

So, the radius of the circle is 6 cm.

t

Example 2: Diameter 15 cm

Let's consider another example where the diameter is 15 cm:

t tt

Start with the given diameter:

tt

Diameter 15 cm

t t tt

Find the radius using the formula:

tt

Radius Diameter / 2 15 cm / 2 7.5 cm

t

Example 3: Diameter 14 cm

Let's solve the problem for a diameter of 14 cm:

t tt

Given diameter:

tt

Diameter 14 cm

t t tt

Apply the formula to find the radius:

tt

Radius Diameter / 2 14 cm / 2 7 cm

t

Calculating the Circumference

Beyond just finding the radius, understanding the relationship between the radius and the diameter is also crucial when calculating the circumference of a circle. The formula for the circumference of a circle is:

t

Circumference 2πr

Where r is the radius of the circle. Let's look at an example of calculating the circumference:

t tt

Consider a circle with a diameter of 12 cm:

t t tt

Find the radius first:

tt

Radius Diameter / 2 12 cm / 2 6 cm

t t tt

Use the formula for the circumference:

tt

Circumference 2πr 2 × (22/7) × 6 264/7 37.7 cm

t

Advanced Example: Diameter 11 cm

Here's a final example where the diameter is 11 cm:

t tt

Given diameter:

tt

Diameter 11 cm

t t tt

Find the radius using the formula:

tt

Radius Diameter / 2 11 cm / 2 5.5 cm

t

Conclusion

Understanding the relationship between the diameter and radius of a circle is key to solving various geometry problems. Using the simple formula Radius Diameter / 2, we can easily find the radius of a circle given its diameter. Additionally, this relationship is essential for calculating the circumference of a circle using the formula Circumference 2πr.

Whether you're working on a geometry assignment or need to apply these concepts in real life, this knowledge will serve you well.