Draw a circle of radius r on a 1/2 cm graph paper, and then on a 2mm graph paper. Estimate the area enclosed in each case by actually counting the squares. Now try out with circles of different radii. Establish the pattern, if any, between the two observed values and the theoretical value (area = πr2). Any modifications ?

Asked by mahapatramamata76 | 24th May, 2016, 12:36: PM

Expert Answer:

 
A space c i r c l e space o f space r a d i u s space 2 space c m space i s space d r a w n space u sin g space b o t h space 0.5 space c m space g r a p h space p a p e r space a n d space 2 space m m space
g r a p h space p a p e r. space

T o space f i n d space t h e space a r e a space u sin g space g r a p h comma space w e space n e e d space t o space c o u n t space t h e space n u m b e r space o f space s q u a r e s space i n s i d e
t h e space c i r c l e space i n space e a c h space c a s e. space

F o r space s q u a r e s space w h i c h space a r e space n o t space e n t i r e l y space i n s i d e comma space w e space u s e space t h e space f o l l o w i n g space r u l e colon
1. space I f space l e s s space t h a n space h a l f space o f space t h e space s q u a r e space i s space i n s i d e comma space w e space i g n o r e
2. space i f space m o r e space t h a n space h a l f space o f space a space s q u a r e space i s space i n s i d e comma space w e space c o u n t space i t space a s space o n e.

I n space t h e space f i r s t space f i g u r e space comma space a r e a space o f space o n e space s q u a r e space i s space 0.5 cross times 0.5 equals 0.25 space c m squared
I n space t h e space s e c o n d space f i g u r e comma space a r e a space o f space o n e space s q u a r e space i s space 0.2 cross times 0.2 equals 0.04 space c m squared

U sin g space t h e space a b o v e comma space w e space f i n d space t h e space a r e a space o f space t h e space c i r c l e s space i n space b o t h space c a s e s.

T h e space 2 space m m space g r a p h space p a p e r space w i l l space g i v e space m o r e space a c c u r a t e space r e s u l t space t h a n space t h e space 0.5 space c m space g r a p h.

Answered by satyajit samal | 27th May, 2016, 01:03: PM

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