Area of circle

As performed in real lab:

Materials required:

Coloured paper, compass, scale, a pair of scissors, gum, colours

Procedure:

  • Draw a circle of radius r = 4 cm (say) on the paper.
  • Divide the circle into 16 equal parts. [Fig (a)]
  • Cut all the 16 parts and arrange them to get the [Fig (b)].
  • Take any part from any side and further divide it into 2 parts. [Fig (c)]
  • To complete the shape of rectangle arrange these two smaller parts at the corners of the shape obtained in [Fig (b)].
  • Find the length and the breadth of the rectangle so formed [Fig (d)].
  • Find the area of the rectangle.


               

                Fig (a)                                                                            Fig (b)

    

                      Fig (c)                                                                             Fig (d)

As performed in Simulator:

  • Click on scale (between 2 and 3) in workbench to draw circle.
  • Click on the circle to mark 16 sectorials parts & color them differently.
  • Move mouse over each wedge to align them in a row.
  • Click on next button below to color wedges & divide in two group.
  • Click blue group to rotate and align.
  • Drag the blue group and drop over green group to join and form parallelogram.
  • Click on left most wedge to cut it into two parts.
  • Drag the red part and attach to the right end so as to form a rectangle.
  • This is a rectangle whose area can be calculated as (Length x Breadth).

Observations:

  • The students will observe that the area of rectangle  \small \dpi{120} \small \frac{2\times \pi \times r}{2}\times r
  • The students will observe that the rectangle is obtained from parts of circle. Hence area of circle =\small \pi \times r^{2}