Jon is asked to clean a circular radioctive area of radius r. If by the end of each day he cleans half the area that he started with on that day, how much area would have been cleaned at the end of the twentieth day?

Question

19771 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-09T17:25:02

Area cleaned in first day #1/2pir^2#

Area cleaned in 2nd day #(pir^2-1/2pir^2)*1/2=1/4pir^2#

Area cleaned in 3rd day #(1/2pir^2-1/4pir^2)*1/2=1/8pir^2#

Area cleaned in 4th day #(1/4pir^2-1/8pir^2)*1/2=1/16pir^2#

So applying sum of above Geometric series we can calculate the area cleaned at the end of the twentieth day

#(1/2pir^2((1-1/2)^20))/(1-1/2)=((2^20-1)/2^20)pir^2#