## anonymous one year ago two circles have areas of 16pi and 25pi. find the ratio of their circumferences

1. ganeshie8

ratio of areas = $$\dfrac{16\pi}{25\pi} = \dfrac{16}{25}$$ therefore ratio of curcumferences = $$\dfrac{\sqrt{16}}{\sqrt{25}} = \dfrac{4}{5}$$

2. anonymous

thank you!

3. ganeshie8

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 $$\sqrt{a}:\sqrt{b}$$

4. anonymous

so it works for area and circumferenceÉ

5. anonymous

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 :)

6. anonymous

thanks)