Radius of the Circle: Definition, Formula with Solved Examples
In geometry, a radius of a circle is any straight line from the center of the circle to its circumference. The length of the line is called the radius. The plural form of radius is radii. A radius is half the diameter, so it’s also the distance from the center to any point on the edge of the circle. It’s also an important part of many formulas in math and physics. In this article, we’ll discuss the definition of a radius, how to find the radius given different information, and some examples.
What is a circle?
A circle is a two-dimensional figure consisting of all points in a plane that are equidistant from a given point, called the center. The distance from the center to any point on the circle is called the radius. The circumference of a circle is the distance around it. It is equal to c times the radius, where π is approximately 3.14159.
What is the radius of a circle?
The radius of a circle is the distance from its center to its edge. It is also the length of the line segment that joins the center of the circle to any point on its circumference. The formula for calculating the radius of a circle is:
radius = circumference รท 2π
where π is pi, a constant equal to 3.14.
The radius of a circle can be found by measuring the distance from its center to any point on its circumference. For example, if we know the circumference of a circle is 10 feet, we can divide that by 2π to find that its radius is 1.6 feet.
The formula for finding the radius of a circle
A radius is a straight line from the center of a circle to the circumference. The formula for finding the radius of a circle is: r = C/2π. Where C is the circumference and π is 3.14. The radius can also be found by taking the square root of the area divided by π: r = sqrtA/π.
How to find the radius of a circle using the circumference
The radius of a circle can be found using the circumference, which is the distance around the edge of the circle. To find the circumference, you need to know the diameter of the circle, which is the distance across the circle. The formula for circumference is C = πd, where d is the diameter. To find the radius, you can use the formula r = d/2.
An example of how to find the radius of a circle
There are various methods for finding the radius of a circle. One method is to divide the circumference of the circle by 2π. Another method is to find the area of the circle and divide it by π. Yet another method is to draw a line from the center of the circle to one of its edges and measure the length of this line. The radius is half the length of this line.
What is the relationship between the radius and diameter of a circle?
The radius of a circle is the distance from the center of the circle to any point on the edge of the circle. The diameter of a circle is the distance from one side of the circle to the other, or twice the radius. So, the relationship between the radius and diameter of a circle is that the diameter is twice the radius.
Properties of a circle
A circle is a two-dimensional closed curve. Every point on the curve is equidistant from the center of the circle. The distance from the center to any point on the curve is called the radius of the circle. The perimeter of a circle is called its circumference.
The following are some of the properties of a circle:
The radius of a circle is always positive.
The diameter of a circle is twice the radius.
The circumference of a circle is 2πr, where r is the radius.
The area of a circle is πr^2, where r is the radius.
Circle Formulas
There are various formulas associated with a circle. The most commonly used formula is the one that gives the relationship between the circumference and diameter of a circle. This formula is:
C = πd
where C is the circumference and d is the diameter.
Other important formulas involving a circle are those that give the area and the radius of a circle. The formula for the area of a circle is:
A = πr^2
where r is the radius of the circle. Similarly, the formula for finding the radius of a circle when its area is known is:
r = sqrt(A/π)
Conclusion
In this blog, we learned about the radius of a circle, its definition, and formula. We also looked at some solved examples to understand the concept better.
The radius of a circle is the distance from the center of the circle to any point on the edge of the circle. The formula for calculating the radius of a circle is r = d/2, where d is the diameter of the circle.
The radius of a circle can be used to calculate other measures, such as the circumference and area. To calculate the circumference, use the formula C = 2πr. To calculate the area, use the formula A = πr2.
Solved examples are a great way to learn how to apply a concept. In this blog, we looked at two examples: one that involved calculating the radius and one that involved finding the missing values given certain information about a circle’s radius.
I hope this blog was helpful in understanding what the radius of a circle is and how to calculate it!
Frequently Asked Questions
A radius is a line segment that joins the center of a circle to any point on its circumference. The plural form of radius is radii. A common length unit for a radius is inches, feet, or meters.
The formula for the radius of a circle is r = C/2π. To use this formula, substitute the circumference of the circle in place of C. For example, if the circumference of a circle is 20 inches, then the radius would be 10 inches (r = 20/2?).
If you know the diameter of a circle, you can also find the radius. The diameter is twice the length of the radius, so to find the radius divide the diameter by 2. For example, if the diameter of a circle is 10 inches, then the radius would be 5 inches (diameter/2 = 10/2 = 5).
Here are some solved examples using the formula for finding the radius of a circle:
1) Find the radius of a circle with a circumference of 6.28 feet.
Radius = Circumference/2π
Radius = 6.28/2π
Radius = 1 foot
2) Find the radius of a circle whose circumference is 15 meters.
Radius=Circumference/2π
Radius=15m/2π
Radius=2.36m
