Two circles have circumferences of #\pi# and #3\pi#. What is the ratio of the area of the circles? the diameters? the radii?

1 Answer
sankarankalyanam
Oct 7, 2017

Ratio of circumferences, radii and diameter #=1/3#
Ratio of areas #=1/9#

Explanation:

Let the radius of the two cities be R1 & R2.
Then circumference of the two circles will be #2pi(R1)# & #2pi(R2)#
Ratio of circumferences will be
#(2pi(R1))/(2pi(R2))=pi/(3pi)=1/3#
#:.(R1)/(R2)=1/3#
1) Ratio of radii#(R1)/(R2)=1/3#

2) Ratio of diameters #(2*(R1))/(2*(R2))=(R1)/(R2)=1/3#

3) Ratio of area of circles is
#(pi(R1)^2)/(pi(R2)^2)=(R1)^2/(R2)^2#
#=((R1)/(R2)).((R1)/(R2))=(1/3)*(1/3)=1/9#

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