How to find the radius of a circle from its diameter and circumference

This post is to explore two methods on how to find the radius of a circle. In most cases radius of the circle is given in the problem and students are asked to find the area of a circle or the circumference of the circle. Still there are certain problems where students have to find the radius of a circle.

First of all let’s define the radius of the circle. The definition of the radius is given below:

“The fixed distance from center to the circumference of a circle is called its radius”.

Radius is also defined as half of the diameter of the circle.

How to find the radius of a circle?

When it comes to find the radius of a circle, there are three types of questions which can ask about how to find the radius of a circle. Most of the secondary school math syllabuses contain such types of problems about circles. All the three types have been discussed at this site step by step. Two methods are given below:

Many circle geometry problems involve finding circumference and area of a circle when the diameter of the circle is given in the question. Many students don’t like to use the diameter in the formulas of circumference and area of the circle. Instead they prefer to use the formulas with radius.

In such situations, students have to find the radius of the circle from its diameter. There is an easy step to convert the diameter into radius. As said earlier, the radius is half the diameter; so divide the diameter by 2 to get the radius of the circle.

For example; find the circumference and area of a circle with diameter of 12 cm.

To solve above problem we’ll use the radius in the circle formulas. But radius is unknown at this stage. Need not to worry, we are given with the diameter and divide it by 2 to get radius as shown below:

Diameter “d” = 12 cm

Radius “r” = 12 ÷ 2 = 6 cm

Now formula for the circumference of the circle is as given below:

C = 2 x 3.14 x 6 = 37.68cm

Similarly we can find the area of the circle using the following formula

Hence, the method to find the radius of a circle from its diameter and then use radius to find the area and circumference of the circle.

2. Finding radius of a circle when the circumference of this circle is given.

The second type of problems asking to find the radius of a circle, when its circumference is given. In such situation the formula to find the circumference and the reverse engineering is used to find the radius.

For example; let’s find the radius of a circle whose circumference is given to be 21 meters.

First of all let’s write the given circumference of the circle using math representation, as shown below;

Circumference “C” = 21 cm

Now replace “C” by the formula to find the circumference using radius. In other words replace “C” by as shown below:

Hence radius r = 3.7 cm  (rounded to one decimal place)

Hence the radius of a circle, whose circumference is given to be 21 m, is 3.7 m.

For more information on mathematics content standards and what kids should learn when, click the previous link to download these standard sheets from government site.

That's all about how to find the radius of a circle when its diameter or circumference is given.

Finding Radius When Area Of A Circle Is Given

In previous post we explain that how to find the radius of a circle when its diameter and circumference is given. This post is to explain how to find the radius of a circle when its area is given. To do this task students need to know the square root a number.

The square root is inverse operation of the square. In formula to find the area of a circle, we need to square the radius.

When area of the circle is given and you need to find its radius, you have to divide the area by ? (pi) and then square root of the result to find the radius of this circle.

Examples to find radius of a circle from its area

For example; find the radius of a circle with area of 314 sq.cm

To solve this problem, consider the letter “r” denotes the radius of the circle and “A” represents the area of the circle.

Hence the radius of a circle with area of 314 sq.cm is calculated to be 10 cm.

Example 2: Find the radius of a circle whose area is 57 sq.in

Again we use the letter "r" to represent the radius of the circle and letter "A" to represent the area of the circle and solve for the radius "r" as explained below:

Hence the radius of a circle with area of 57 square inches is calculated to be 4.26 inches. Hope that both the examples have well explained the concepts of finding radius when the area of a circle is given.