Question

If ratio of areas of two circles are 4:9, then what is the ratio of their circumference?

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Answer 1

Step-by-step explanation:

Area 1 / Area 2

π r1^2 /π r2^2

r1 ^2 / r2 ^2 = 4/9

9 r1 ^2 = 4 r2 ^2

taking square root

3r1 = 2 r2

r2 = 3/2 r1

2πr1 / 2 π r2

1 / 3/2

= 2/3

Hope it helps uh!

Answer 2

Given:

Ratios of two circles are 4:9

To Find:

What is the ratio of their circumference

Solution:

As we know the formula for the area of a circle is

                                      $A=\pi r^{2}$

where,

          r= radius of the circle

And the formula for the circumference of a circle is

                                      $C=2\pi r$

where,

          r= radius of the circle

Now, let the radius of the two circles be r1 and r2 and using the ratios properties we will express the equation as,

$\frac{\pi r_{1}^2}{\pi r_{2}^2} =\frac{4}{9} \\\frac{r_{1}}{r_{2}} =\frac{2}{3}$

Now using this value of r1/r2 to find the ratio of the circumference of the circle, putting it as a ratio with the formula we have

$=\frac{2\pi r_{1}}{2\pi r_{2}} \\=\frac{r_{1}}{r_{2}} \\=\frac{2}{3}$

Now because we were only left with r1/r2 we straight forward put the value as 2/3 which is the ratio of their circumference

Hence, the ratio of the circumference of the circle with areas as 4/9 is 2:3.