Area of Circle Formula

Area of circle formula

Area of circle can be found out by multiplying r² by pi.Here pi represents the constant ratio of circumference to diameter of any circle which is approximately equal to 3.14159. The area of the circle formula is useful when there is a need to know how much commodity will be required to cover a circular plot. Thus we can say the space covered within the boundary of a circle is called area of circle.Suppose, there is a circular bed then this formula will help us to know how much bed sheet is needed to cover it completely.

To find the area of circle first let’s discuss some terminologies related to circle which will be useful in formula

1. Diameter = The diameter is the length of the line through the centre that touches 2 points on the edges of the circle.

2. Radius = the half of diameter can be called radius or we can say that the line extends from the centre of the circle to the circumference of the circle is called radius.

3. Circumference  = circumference is the distance that surrounds the circle.

Area of circle can be calculated by using following formulas:

1. Area of circle = πr²( when radius is given)

              Π = constant ratio(3.14159)

               r = radius of circle

2. Area of circle = (π/4) × d²

              D = diameter of circle

3. Area of circle = 2πr

C = circumference of circle

Examples

1. Find the area of the circle whose radius is 10 mm?

A = πr²

A = 3.14 * 10²

A = 3.14 * 10 * 10

A = 314mm²

So, the area of circle is 314mm²

2. The area of a circle is 50.24 square yards. What is the radius of the circle?

A = πr²

50.24 = 3.14 r²

50.24/3.14 = r²

r² = 16

r = -4 , 4

Since the r cannot be taken as negative , we will consider the answer which is positive, that is 4. 

Example 3: The length of the largest chord of a circle is 14 units. Find the area of the circle.

Solution:

Diameter(d) = 12 units(given)

Using the formula for the circle’s area,

Area of a Circle = (π/4)×d²

Put the values,

A = (π/4) × 14²

A = (π/4) × 196

A = 249.68

Answer: The area of the circle is 249.68 square units

Example 4

A circle has a radius of 8 cm. Calculate its diameter, area and circumference.

Solution

Given parameters are,

Radius, r = 8cm

Diameter of a circle is given by

2r

= 2 × 8 cm

= 16 cm

Area of a circle is given by

π r²

= π × 64

= 201.088 cm²

Circumference of a circle is given by

2 π r

= 2 × π × 8

= 50.272 cm