Area of Circle
introduction
-From this applet , we show area of circle by dynamic figure.
-In this applet at first we draw a circle and it divides many pics like triangle.
if you move slider n, then the circle divided into many pics like a triangle and it arranged itself a Rectangle.
-where circumference of circle arranged in length and the radios of circle arranged in breadth.
so, the area of circle is=Area of Rectangle
=length *Breadth
=Pi r*r
=Pi r^2.
Objectives
Design an applet to show Area of Circle .
User Guidelines
1) Move the slider r then you see circle with different radius.
2)Move the slider n then you see a circle divided into many parts like triangle and also you see the arranged rectangle which is made from the many pics of triangle.
3)This arranged rectangle gives the area of circle .
Where, Pi r=Circumference of circle =Length of Rectangle
r=Radius of circle =Breadth of rectangle
so, area of Circle =Area of Rectangle
=length*bredth
=Pi r*r
=Pi r^2
applet
Test Your Understandings
By studying above applet , which of t he following formula indicate the area of circle.
Select all that apply
- A
- B
- C
- D
Construction Protocol
1. Open a new GoeGebra window.
2.Create a number slider r by using slider tool.(max-4,min 1 and increment 1)
3. Again create a number slider n by using slider tool where, min -4, max-60 or you can put any number.
4.Draw point A in +y-Axesby using point tool.
5.create a circle through center point A and radius r.( if you move slider r then there becomes circle with different Radius.)
6.Create a point B in anywhere of the circumference of circle.
7.Input Rotate(B,360/n,A) by input tool which gives B'
8 Join line segment BB'. by segment tool.
9.Draw mid point between the line segment BB' named it by C.
10. join line segment AC by segment tool.
11.Rename the segment BC by dx and Ac by dy.
12. Input L1: Sequence (Rotate(B,j 360/n,A),j,0,n)
L2: Sequence(Circular sector(A,Element(L1,j),Element(L1,j+1),j,1,n,2)
L3=Sequence (Circular sector(A,Element(L1,j),Element(L1,j+1),j,2,n,2)
L4=Sequence (Circular sector ((j dx,0),jdx+dx/2,dy),(jdx+(-dx)/2,dy)),j,1,n/2-1)
L5=Sequence(Circular sector((j dx+dx/2,dy),(j dx+0,0),jdx+dx,0)),j,0,n/2-1)
13.Hide the objects dx,dy and C.
14.color the object L3 and L4 by same color and object L4 and L5 by same color.(by object properties.)
15.insert the dynamic text Pi r on the length of rectangle and insert the dynamic text r for breadth of rectangle and decorate it by using object properties .
17 insert dynamic text Area of circle = pi r*r
= Pi r^2.
At last save your ggb file