# Area of circle

From Karnataka Open Educational Resources

### Introduction

Area of a circle is the surface occupied by the circle in a 2-dimensional plane. The area of a circle is given by the formula,

Area of circle = πr^{2}, where r is the radius of the circle and constant ratio π =

This area of the circle can be found by two methods-

- A circle of given radius can be drawn on the graph sheet (Fig.1) and the rough estimate its area can be found by counting the number of squares enclosed.
- By dividing the circle into a number of sectors which when arranged forms a parallelogram. Then the area of the parallelogram(rectangle) gives the area of the circle.(as shown below)

### Objectives

To enable students to-

- understand how the area of a circle can be obtained with the help of area of parallelogram(rectangle);
- derive the formula for the area of circle;
- verify the formula for the various values of the radius.
- solve problems related to area of circle.

### Prerequisites/Instructions, prior preparations, if any

Recall concept of area of a plane figure, circle and its parts.

### Process (How to do the activity?)

#### Teaching Resource

Geogebra File:Area of circle.ggb

Download this geogebra file from this link.

- Identify various given shapes.
- Identify the radius, diameter, sector of the circle.
- What is the relationship between circumference and diameter/radius of a circle?
- Draw a circle and divide it into a number of sectors.
- Show that the sectors when arranged forms a parallelogram(rectangle)
- What is the breadth of the rectangle formed using the sectors of the circle?
- What is the length of the rectangle formed using the sectors of the circle?
- Is the length complete circumference or half circumference of the circle?
- How to find the area of a rectangle?
- Verify for different radii or number of sectors of the circle and analyze the results.

#### Evaluation

- Find the area of circular pizza of radius 15 cm.
- If the circumference of a circular sheet is 154m, find its radius. Also find the area of the sheet.