When working with circles, we often come across terms like 'radius', 'diameter', 'circumference', and 'area'. These are all closely related, and their values can be derived from one another. Let's see how to calculate the radius of a circle depending on the given values.

What is the radius of a circle?

The radius of a circle is the distance from the center of the circle to a point on the circle. In mathematical terms, the radius is usually represented by the letter r.

Calculate radius when the diameter is known

If the diameter of the circle is given, calculating the radius is straightforward. The diameter of a circle is simply twice the radius. So, to find the radius, we divide the diameter by 2:

r = d / 2

Where:

r is the radius of the circle

d is the diameter of the circle

Calculate radius when the circumference is known

If the circumference of the circle is given, the radius can also be calculated. The circumference of a circle is calculated by multiplying the diameter of the circle by pi (a mathematical constant approximately equal to 3.14159). So, to calculate the radius from the circumference, we use the formula:

r = C / (2 * pi)

Where:

r is the radius of the circle

C is the circumference of the circle

pi is a mathematical constant (~3.14159)

Calculate radius when the area is known

If the area of the circle is given, the radius can also be calculated. The area of a circle is calculated by squaring the radius and multiplying it by pi. So, to calculate the radius from the area, we use the formula:

r = √(A / pi)

Where:

r is the radius of the circle

A is the area of the circle

pi is a mathematical constant (~3.14159)

√() represents the square root function

Therefore, calculating the radius of a circle is a matter of knowing and applying the correct formula, depending on the given values.