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Maths Formulas

Radius Formula

Many objects in our daily life in round shape. Some objects of this shape are wheels of a vehicle, bangles, clocks, coins etc. Geometrically such objects are called a circle in 2-D and sphere in 3-D. These objects are having one fixed point in the body known as the centre. Distance from centre to the endpoint on the boundary is referred to as radius. In this article, we will discuss radius circles, some other related terms and radius formula with examples. Let’s start learning!

Radius Formula

What is the Radius?

A circle is a particular shape of the objects. A circle is a type of closed shape. It is the set of all points in a plane which are at a given distance from a given point. So, the distance from the centre the circumference is a constant, which is known as the radius of the circle. Therefore, we may connect a point on the circumference on a circle to the given centre. Then the line segment made will be the radius of the ring. We can easily derive at the radius by dividing the diameter of the circle by 2.

We can also compute the radius if we know the length of the circumference of the circle or area of the circle. Thus a unique circle will have a unique value of radius.

Radius Formula

(Source: Wikipedia)

Some terms related to a circle are as follows:

  1. Centre: It is a point as a pivot in the circle.
  2. Circumference: It is the set of points that are at an equal distance around the centre of the circle.
  3. Radius: It is the distance from the centre to any point on the circumference.
  4. Diameter: It is the distance between any two points on the circumference measured through the centre. It is double in the length that the length of the radius.
  5. Area: Area of the circle describes the amount of space covered by the circle. So, it will give the coverage of circle as a two-dimensional plane.

Formulas for Radius:

Let us now discuss the different methods to compute the radius of a circle by studying the radius formula. We need anyone value out of its diameter, circumference or area. The formula in terms of diameter, circumference, and the area is as follows:

If we know the diameter,

\(R = \frac {D}{2}\)

If we know the circumference,

R = \(\frac{C}{4\times \pi}\)

If we know the area of the circle,

R = \(\sqrt(\frac{A}{\pi}\)

R the radius of the circle
D the diameter of the circle
A the area of the circle
\(\pi\) 3.14
C Circumference of circle

Solved Examples

Q.1: Find the radius of the circle whose diameter is 15 cm?

Solution: As given in the problem,

Diameter of the circle, D = 15 cm

Thus using the formula,

\(R = \frac {D} {2}\)

Substituting the value of diameter,

\(R = \frac {15} {2}\)

R = 7.5 cm

Q.2: Find the radius of the circle whose area is 300 square cm?

Solution: As given in the problem,

Area of the circle, A = 300 square cm

Now applying the formula,

\(R = \sqrt(\frac{A}{\pi}\)

Substituting the value of are we get,

\(R = \sqrt(\frac{300}{\pi}\)

= \(\sqrt(\frac{300}{3.14}\)

= 9.77 cm

Thus radius is 9.77 cm.

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