Lab Manual: Area of Circle by Coiling Method | Lab Manuals for Class 10 PDF Download

Objective

Prerequisite Knowledge
(i) Definition of circle: A circle is the locus of a point in a plane which moves in such a way that its distance from a fixed point remains constant. Fixed point is known as centre and the fixed distance is known as radius of the circle.
(ii) Area of the circle: It is the measure of the region of a plane enclosed by it.
(iii) Circumference of the circle: Total length of its boundary
(C = 2πr, where r is radius of the circle)
(iv) Area of triangle: 1/2 x Base x height
(v) Concentric circles: Circles having same centre.

Materials Required
Thick string or coloured threads, cutter, a pair of scissors, fevicol, geometry box.

Procedure

• Construct a circle of radius r, (take r = 3.5 cm) using compass and draw concentric circles of smaller radius as shown in fig. (i).
  
• Fill the area of drawn circle with concentric circles made of different coloured strings or thread, so that there is no gap between the threads as shown in fig. (ii).
• Last smallest circle be a point circle.
• With the help of scissors, cut the coloured circular threads along the radius OA.
• Open all the threads and arrange each thread as a straight line.
• Place each thread one over another starting from thread of the largest circle to the | smallest circle in such a way that it forms a triangular shape as shown in fig. (iii).
  

Observation

• The triangular shape so formed out of the threads, area of the circle is the same as the area of triangular shaped.
• Base of the triangle is the circumference of the circle (The largest thread) i.e. Base of ∆ = 2πr
• Vertical height of the triangular shape = radius of the circle.
• Area of ∆ = 1/2  x  B  x  H
  = 1/2 x 2πr x r
  = πr²
  ∴ area of the circle of radius r = πr²

Result
The figure formed in this activity is almost the shape of the triangle, therefore the area of this triangle so formed is equal to the area of the circle i.e. πr2 sq. units.

Learning Outcome
Students observe that the area of the circle is πr2 i.e. half the product of its circumference and radius.

Activity Time

• Using the above activity find the area of circle taking radius as 4.2 cm.
• Using the above activity find the area of circle taking radius as 4.9 cm.