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Radius Formula
The Radius Formula is a line segment that connects the centre to the perimeter of a circle or sphere. The radius length remains constant from the centre to any point on the circle or sphere’s perimeter. It is half the diameter’s length.
What is Radius?
The Radius Formula is defined in geometry as a line segment from the centre of a circle or sphere to its perimeter or border. It is a circle and sphere component that is frequently abbreviated as ‘r.’ When discussing more than one radius at a time, the plural of radius is “radii.” The diameter of a circle or sphere is the longest line segment connecting all points on the opposite side of the centre, while the radius is half the length of the diameter. It’s written as d/2, where d is the diameter of the circle or sphere.
Radius Formulas
The radius of a circle and sphere may be computed using certain special formulae that one will learn in this section. Students will discuss the Radius Formula for circles in this section. The radius of a sphere formula is addressed more on the Extramarks website.
The Radius Formula based on Diameter:
The diameter is a straight line that connects a point at one end of the circle to a point at the other end of the circle. The radius is twice as long as the diameter. Diameter = 2 radius is the mathematical formula. It is also the circle’s longest chord.
The Radius Formula = Diameter/2 or D/2 units
Circumference Radius Formula
The circumference of a circle is its perimeter. It is the circumference of a circle and may be stated as C = 2r units. C is the circumference of the circle, r is the radius of the circle, and is the constant equal to 3.14159. The radius is defined as the circumference divided by two. The Radius Formula utilising a circle’s circumference is as follows:
The Radius Formula = Circumference/2π or C/2π units
The Radius Formula with Area
The area of a circle is the space that it occupies. The formula Area of the circle = r2 square units expresses the connection between radius and area. Here, r is the radius and is a constant equal to 3.14159. The Radius Formula based on circular area is as follows
The Radius Formula = √(Area/π) units
Radius of Circle
One of the most significant aspects of a circle is its radius. It is the measurement of the distance between the circle’s centre and any point on its perimeter. In other terms, the radius of a circle is the straight line segment that connects the centre of a circle to any point on its perimeter. Because there are infinite points on a circle’s circumference, it can have more than one radius. This signifies that a circle has an endless number of radii and that all of the radii are equidistant from the circle’s centre. When the radius of the circle changes, the size of the circle changes.
How to Find the Radius of a Circle?
When the diameter, area, or circumference of a circle are known, the radius may be calculated using one of the three fundamentals of the Radius Formula. Students apply these formulas to calculate the radius of a circle.
The Radius Formula = Diameter/ 2 is the formula when the diameter is known.
The Radius Formula = Circumference/2π when the circumference is known.
When the area of the circle is known, the radius is calculated as
The Radius Formula =(Area of the circle/π).
Radius of Circle Equation
A circle is a closed curve formed from a set point known as the centre, with all points on the curve being the same distance from the centre point. The equation for a circle with (h, k) centre and radius r is as follows:
r2=(xh)2 + (yk)2
This is the equation’s standard form. Thus, if students know the coordinates of the circle’s centre and radius, they can simply derive its equation.
Radius of a Sphere
A sphere is a threedimensional solid figure. The radius of a sphere is the distance from the centre to any point on the sphere’s edge. It is a decisive factor when sketching a sphere since its size is determined by its radius. A sphere, like a circle, can have an endless number of radii that are all the same length. We need to know the radius of the sphere to compute its volume and surface area. Students can also simply compute the radius of a sphere using the volume and surface area calculations.
Radius of Circle Examples
Mathematics is one of the most challenging and highscoring subjects. Students that use Extramarks examples can improve their studies and achieve their objectives. These Extramarks solved examples have been carefully selected to assist students in learning and understanding the Radius Formula. The language is simple to understand, allowing students to learn more and benefit more fully.
Practice Questions on Radius of Circle
Conceptual clarity is required for students to do effectively on tests or competitive exams. As a result, Extramarks offers students with instances of the Radius Formula. They can quickly pick up new knowledge and fully grasp the study topic. Learning Mathematics requires studying and comprehending topics, as well as practising questions based on the Radius Formula concepts.
FAQs (Frequently Asked Questions)
1. What is the Geometric Radius of a Circle?
The radius of a circle is the length of the line segment from the circle’s centre to a point on its perimeter. It is commonly shortened as ‘r.’ A circle can have an unlimited number of radii, all of which have the same length. It is half the circle’s diameter.
2. What is the Radius?
A circle is one of the items’ shapes. A circle is an enclosed form. It is the collection of all points in a plane that are a particular distance from another point. As a result, the radius of the circle is defined as the distance from the centre of the circumference. As a result, students may connect a point on a circle’s perimeter to the supplied centre. The radius of the ring will then be determined by the line segment created.