A wire of length L can be shaped in to a circle or a square the ratio of area of a square divided by the area of circle is ??

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2 Answers
iceman
Jul 6, 2018

#pi/4#

Explanation:

Wire of length = L, shaped into a square then the perimeter of square is:
#P=L# => perimeter of square is 4 times the length of a side:
#P=4s# => then:
#s=P/4=L/4# => next the area of square we call #A_1#is:
#A_1#=#s^2=(L/4)^2=L^2/16#

Now for the circle we get:
#C=2*pi*r=L# => then the radius is:
#r=L/(2pi)# => the area of circle we call #A_2# is:
#A_2#=#pir^2=pi*[L/(2pi)]^2=L^2/(4pi)#

Finally the ratio of area of square divided by the area of the circle is:
#A_1/A_2##=[L^2/(16)]/[L^2/(4pi)]=pi/4#

Narad T.
Jul 6, 2018

The ratio is #=pi/4#

Explanation:

The circumference of the circle is

#2pir=L#

The radius is #r=L/(2pi)#

The area of the circle is

#A_c=pir^2=pi*(L/(2pi))^2=piL^2/(4pi^2)#

#=L^2/(4pi)#

The length of each side of the square is

#l=L/4#

The area of the square is

#A_s=l^2=(L/4)^2=L^2/16#

The ratio is

#A_s/A_c=(L^2/16)/(L^2/(4pi))=pi/4#

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