Geometry

Area of Circle Formula

Learn the Area of Circle Formula with explanation, derivation, solved examples, practice questions, and downloadable notes.

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Area of Circle Formula

Formula

A = πr²

Where A = Area, r = Radius of the circle

Formula Variables

Symbol Meaning
A Area of the Circle
π Pi (3.14159 or 22/7)
r Radius of the Circle

What is the Area of Circle Formula?

The Area of a Circle Formula is used to calculate the total space enclosed by the circumference of a circle. It is one of the most fundamental formulas in geometry and is widely used in mathematics, engineering, construction, architecture, and everyday calculations.

The area depends only on the radius of the circle. As the radius increases, the area increases proportionally to the square of the radius.

Formula:

A = πr²

Formula Derivation

Imagine cutting a circle into several equal sectors and arranging those sectors alternately.

The resulting shape resembles a rectangle where:

  • Length = πr
  • Width = r

Therefore,

Area = Length × Width

= πr × r

= πr²

Where is this Formula Used?

  • Geometry Problems
  • Competitive Exams
  • Engineering Calculations
  • Construction Projects
  • Architecture
  • Physics
  • Mathematics
  • Measurement Calculations

Solved Example

Question: Find the area of a circle whose radius is 7 cm.

Given:

Radius = 7 cm


Formula:

A = πr²

= 22/7 × 7 × 7

= 154 cm²

Practice Questions

Question 1

Find the area of a circle whose radius is 5 cm.

Question 2

Calculate the area of a circle having a radius of 14 cm.

Question 3

A circular garden has a radius of 21 m. Find its area.

Question 4

Find the radius of a circle whose area is 154 cm².

Important Notes

  • ✅ Area is always measured in square units.
  • ✅ Radius is half of the diameter.
  • ✅ Use π = 22/7 or 3.14159.
  • ✅ Area cannot be negative.
  • ✅ Radius must always be positive.
  • ✅ Diameter = 2 × Radius.

Common Mistakes

  • Using diameter instead of radius directly.
  • Forgetting to square the radius.
  • Using incorrect value of π.
  • Writing the answer without square units.

Quick Revision

Formula A = πr²
Radius Distance from center to circumference.
Diameter 2 × Radius
Unit Square Units (cm², m², km²)
Category Geometry

Frequently Asked Questions

The Area of Circle Formula is A = πr².

π (Pi) is approximately equal to 3.14159 or 22/7.

Area is always expressed in square units like cm², m², km².

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