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→Activities
Use the GeoGebra file [[http://rmsa.karnatakaeducation.org.in/sites/rmsa.karnatakaeducation.org.in/files/documents/Constant_Pi.html]] and illustrate and verify that the ratio is true for different radius by moving the radius slider and using the table below to compute the values.
Use the GeoGebra file [[http://rmsa.karnatakaeducation.org.in/sites/rmsa.karnatakaeducation.org.in/files/documents/Constant_Pi.html]] and illustrate and verify that the ratio is true for different radius by moving the radius slider and using the table below to compute the values.
[[Image:KOER%20Circles_html_14d27306.png|650px|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_14d27306.png]]
[[Image:KOER%20Circles_html_14d27306.png|650px|link=]]
[[Image:KOER%20Circles_html_7b6eda1c.png|650px|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_7b6eda1c.png]]
[[Image:KOER%20Circles_html_7b6eda1c.png|650px|link=]]
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==== Perimeter of a circle ====
=====Learning Objectives=====
To apply the use of calculating the perimeter of a circle in a real life example .
====Material and Resources Required====
Pencil, Paper
====Pre-requisites/Instructions====
Draw the following sketch and do the calculations for the evaluation questions. The sketch shows the two main dimensions of a standard 400 metres running track.
[[Image:KOER%20Circles_html_m210a6c46.png|650px|link=https://karnatakaeducation.org.in/KOER/en/index.php/File:KOER_Circles_html_m210a6c46.png]]
====Evaluation====
#Calculate the inside perimeter of this shape.
##'''Why do you think that it is not equal to 400 metres? '''The inside runner cannot run at the very edge of the lane (there is normally an inside kerb) but let us assume that the athlete runs at a constant distance of, say, x cm from the inside edge.
#
#What is the radius of the two circular parts run by the athlete in the inside lane?
#
#Show that the total distance travelled, in centimetres, is 2 π (3650 + x ) + 16878 and equate this to 40 000 cm to find a value for x.
##Is it realistic? For 200 m and 400 m races, the runners run in specified lanes. Clearly, the further out you are the further you have to run, unless the starting positions are staggered.
#
#The width of each lane is 1.22 m, and it is assumed that all runners (except the inside one) run about 20 cm from the inside of their lanes.
##With these assumptions, what distance does the athlete in Lane 2 cover when running one complete lap? Hence deduce the required stagger for a 400 m race.
##What should be the stagger for someone running in Lane 3 ?
#
#If there are 8 runners in the 400 m race, what is the stagger of the athlete in Lane 8
compare with that in Lane 1 ? Is there any advantage in being in Lane 1?
===== Further Explorations =====
1. This link gives an overview of what Pi is. [[http://en.wikipedia.org/wiki/Pi]]
=== Concept #2 Terms associated with circles ===
=== Concept #2 Terms associated with circles ===