The ratio of their area is 9/4
We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:
[tex]3:2[/tex]
and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:
[tex]C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle[/tex]
If we define:
[tex]C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2[/tex]
Then, the ratio of the circumference of two circles is 3:2 is:
[tex]\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}[/tex]
The area of a circle is given by:
[tex]A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius[/tex]
So the ratio of their area can be found as:
[tex]\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2[/tex]
So:
[tex]\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}[/tex]
Unit rate: https://brainly.com/question/13771948#
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