Question

two circles have areas of 16pi and 25pi. find the ratio of their circumferences

Answer 1

ratio of areas = \(\dfrac{16\pi}{25\pi} = \dfrac{16}{25}\)

therefore ratio of curcumferences = \(\dfrac{\sqrt{16}}{\sqrt{25}} = \dfrac{4}{5}\)

Answer 2

thank you!

Answer 3

Yw, that works more generally. You may use it for any kind of lengths :

If the "areas" of similar figures are in ratio \(a:b\), then the ratio of their "lengths" will be in ratio \(\sqrt{a}:\sqrt{b}\)

Answer 4

so it works for area and circumferenceÉ

Answer 5

1st cirlcle area=>pi r*r=16pi
,so r*r=16 and r=4
similarly ,2nd circle area=> pi*r*r=25pi
so,r=5

circumference of 1st circle=>2 pi*r
so,area =2*pi*4

similarly 2nd area of circle => 2*pi*5

dividing both of them we will get=> 2*pi*4/2*pi*5=4/5
so,ratio is 4/5
:)

Answer 6

thanks)