Area Two Concentric Circles

 

ABOUT:

Circle

A circle is a set of all points that are at a equal distance from a fixed point in a given plane.

Center and Radius

The fixed point is termed as the center of the circle and the common equal distance is known as the radius

Concentric circles

Definition 1: Concentric circles are circles of different sizes and those circles that have a common center i.e., they have same center but different radius.

Definition 2: When two or more circles have the same center but have different radii, they are called as concentric circles, i.e., circles with common center.

Annulus

The area or region which is enclosed between two concentric circles is known as annulus or circular ring.

To find the area of the annulus we need to subtract area of smaller circle from the area of bigger circle

FORMULA:

Area of annulus = [area of bigger circle - area of small circle] m2

DEMONSTRATION:

A fountain which is in concentric shape has two radius one is 7 m and the other is 17 m. calculate the area between the two circles. 

Solution: Let small circle radius = 7 m 
Then big circle radius = 17 m
Area of small circle, a= pi *r2 = 3.14 *7 *7 m= 153.86 m2
Area of bigger circle, A = pi *R2 = 3.14 *17 *17 m= 907.46m2
Area of enclosed region is (907.46-153.86) m2 = 753.6m²