Question

The area of two circles
are in the ratio 49:64.
find the ratio of their
circumferences​

Answer 1

You know that the area of a circle is π r2 and it's circumference is 2πr.

Let the first circle have radius r1 and the second circle have radius r2.

TO FIND: Ratio of circumferences, that is:

2πr12πr2

=\cancel2πr1\cancel2πr2

=r1r2

Now, we are given that the ratio of areas is

πr21πr22=4964

\cancelπr21\cancelπr22=4964

r21r22=7282

(r1r2)2=(78)2

Taking square root on both sides:

r1r2=78