Question

How can you find the radius of a circle from the area?

Answer 1

Hint:
Recall that the area of a circle with radius r units, is given by the formula: Area = $ \pi {{r}^{2}} $ square units. From this equation, our goal is to get only 'r' on the RHS. How can this be achieved? This can be done in exactly the same way we solve a linear equation in one variable. List down the steps one by one.

Complete Step by step Solution:
Let's start with the relation: Area = $ \pi {{r}^{2}} $ , where r is the radius of the circle. Our goal is to find the value of r.
Step 1: Divide both sides of the above equation by π.
⇒ $ {{r}^{2}} $ = $ \dfrac{Area}{\pi } $
Step 2: Taking the positive square root of both sides (since radius cannot be negative), we get:
⇒ r = $ \sqrt{\dfrac{Area}{\pi }} $ , which is the required expression for r in terms of the area.

The answer will be in the same units in which we considered the area.

Note:
A circle is a geometric figure in which all the points are at a fixed distance 'r' from a fixed point 'O'. The distance 'r' is called the radius and the point 'O' is called the center of the circle.
The ratio of the circumference of a circle to its diameter is fixed and its value is 3.14159... which is symbolically represented as π. Therefore, circumference = π × diameter = 2π × radius.