Area of circle

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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 = πr2, where r is the radius of the circle and constant ratio π =

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

Fig.1. Area of circle
  1. 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.
  2. 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-

  1. understand how the area of a circle can be obtained with the help of area of parallelogram(rectangle);
  2. derive the formula for the area of circle;
  3. verify the formula for the various values of the radius.
  4. 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

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