Question

What is the area between the two concentric circles ?

Answer 1

Hint: Here in this question we have to define the area between the two concentric circles. So firstly we know the definition of circle and concentric circle. Then we define the area between the two concentric circles. Hence this will be the required solution for the given question.

Complete step by step answer:
The circle is a closed curve. “A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.” The circles with a common center point are known as concentric circles. In other words. It is defined as two or more circles that have the same center point. The concentric circle is given below.

Here in this figure we have two concentric circles and they have the same center and it is $O$. Both circles have a different radius. The radius of a bigger circle is $R$ and the radius of a smaller circle is $r$.

The region between two concentric circles of different radii is known as an annulus. It is flat – shaped like a ring. The area of the annulus can be calculated by finding the area of the outer circle and the inner circle. We need to find the difference between the areas of both circles to get the result. The shaded part in the above figure shows the annulus.

Note:The area of a circle is different from the area of concentric circles. The area of a circle is given by \[\pi {r^2}\]. The area of concentric circles is given by \[\pi ({R^2} - {r^2})\]. The unit for the area is Square units. To determine the area we use the simple arithmetic operations.