Question

The area of two circles are in the ratio 25:36. Find the ratio of their circumference.​

Answer 1

Step-by-step explanation:

Ratio of areas of circles =25:36

=25/36

Radius of first circle = πr^2

Radius of second circle = πR^2

πr^2/πR^2 = 25/36

r^2/R^2 = 25/36

(r/R)^2 = 25/36

r/R = √25/36

r/R =5/6

Ratio of circumferences=2πr/2πR

=r/R

=5/6

Therefore, ratio of circumferences = 5:6

hope it's helpful to you

Answer 2

Step-by-step explanation:

Let the radii of the two circles be r1 and r2 respictively.

Finding the areas of the two circles

Area of the circle with radius r1=$\pi r\frac{2}{1}$

Area of the circle with radius r2= $\pi r\frac{2}{2}$

Finding the circumference of the two circles

Circumference of the circle with radius $r_{1}= \pi r\frac{2}{2}$

Circumference of the circle with radius $rx_{2} =2 \pi rx_{2}$

Now, it is given in the question that the ratio between the areas of the two circles is 25 : 36

Therefore, $\pi r\frac{2}{1} :\pi r\frac{2}{2}$= 25 : 36

= $\frac{\pi r\frac{2}{1} }{\pi r\frac{2}{2} }= \frac{25}{36}$

$\frac{\pi r\frac{2}{1} }{\pi r\frac{2}{2} }= \frac{5^{2} }{6^{2} }$

$(\frac{r_{1} }{r_{2}})^{2}= (\frac{5}{6})^{2}$

$\frac{r_{1} }{r_{2}}= \frac{5}{6}$

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