Area of circle

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 = $${22 \over 7}$$

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

Teaching Resource
Geogebra File:Area of circle.ggb
 * 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.