Area of a circle

Area of a Circle

• Definition of Area

  • The area of a circle is defined as the amount of space contained within the boundary of the circle.

• Formula for Area of a Circle

  • The area can be calculated using the formula:
    ext{Area} = ext{pi} imes ext{radius}^2

  • This formula can also be represented in a more concise form as:
    A = ext{pi} imes r^2
    where:

  • A = Area

  • r = Radius

  • pi (π) is a mathematical constant approximately equal to 3.14.

• Units of Area

  • The resulting area will be in squared units (e.g., square centimeters, square meters).

• Example Calculation

  • If the radius of the circle is given as 5 centimeters, we can calculate the area as follows:

  1. Substitute the radius into the formula:
     ext{Area} = ext{pi} imes (5 ext{ cm})^2

  2. Calculate the radius squared:
     5^2 = 25 ext{ cm}^2

  3. Multiply by pi:
     ext{Area} = 3.14 imes 25 ext{ cm}^2

  4. Perform the multiplication:
     ext{Area} = 78.5 ext{ cm}^2

• Final Result

  • Therefore, the area of the circle with a radius of 5 centimeters is:
    ext{Area} = 78.5 ext{ cm}^2