Circles

What is the circle?

• The set of all points those are equidistant from a fixed point is called a circle.

• The fixed is called center of the circle.• The line segment between two points on the

circle which is passing through the center is called the diameter.

• The line segment between any point on the circle and the center is called the radius (plural radii).

circle

The fixed point(center)

diameterradius

Circumference:

• The circumference is the length of the outer boundary of a circle.

Finding the circumference

• The circumference of a circle is given by the formula C = πD, where C is the circumference and D is the diameter of a circle.

• Notice that D = 2xRadius = 2r• π : an irrational number which is

approximately equal to 3.14.

Example:

• Find the circumference of each of the following circles.

Find the circumference of each of these circles.

Find the perimeter of each of the shapes below. (Remember to add the lengths of the straight sections.)

A scooter tire has a diameter of 32 cm. What is the perimeter of the tire?

Find the circumference of the Ferris wheel shown below.

Area of a circleIf the circle is divided into smaller sectors, the curved sides of the sectors become straighter and, hence, the shape is closer to a perfect rectangle.

Finding the area of a circle

• The area of a circle, A, can be found using the formula A = π r2 , where π is a constant with a value of approximately 3.14 and r is the radius of the circle.

Example:

• Find the area of each of the following circles.

Find the area of each of these circles.

Find the area of each of the shapes below.

Definition: An annulus (plural annuli) is the shape formed between two circles with a common center (called concentric circles).

Find the area of the annulus for the following sets of concentric circles.

Find the area of the following shapes: