- A circle is a two-dimensional closed figure formed by joining a set of all the points equidistant from a fixed point.
- The fixed point is called the circle's center, and the fixed distance is called the circle's radius.
- The most extended chord that passes through the center of a circle joining the two points on the circumference of a circle, is called its diameter.
, where diameter of the circle & radius of the circle.
- The circumference of a circle is the length of the boundary of a circle, and can be calculated using the formula , where radius of the circle.
- The area of a circle is the measure of the region enclosed inside it.
- The area of a circle depends on the length of its radius.
- If we know the radius of a circle, we can calculate its area using the formula mentioned below.
, where , and the radius of the circle.
- Likewise, if the diameter of a circle is known, its area can be calculated using the formula mentioned below.
, where the diameter of the circle
Example 1: What is the area of a circle with a radius of 7 cm?
Example 2: What is the area of a circle with a diameter of 2 m? (Use )
Example 3: Find the circumference of a circle with a radius of .
- Relation between the diameter & radius of a circle:
- Circumference of a circle:
- Area of a circle when the radius is known:
- Area of a circle when the diameter is known:
- The radius is half of the diameter, not the vice-versa.
- The area of a semi-circle is half the area of a circle.
- The perimeter of a semi-circle is not half the perimeter of a circle.