# A circle has a radius of 9 inches. The radius is multiplied by 2/3 to form a second circle. How is the ratio of the areas related to the ratio of the radii?

${r}_{1} = 9$
${r}_{2} = 9 \cdot \frac{2}{3} = 6$
${r}_{1} / {r}_{2} = \frac{9}{6} = \frac{3}{2}$
The area of a circle is $\pi \cdot {r}^{2}$
$\implies {a}_{1} / {a}_{2} = \frac{\pi \cdot {9}^{2}}{\pi \cdot {6}^{2}} = {\left(\frac{9}{6}\right)}^{2} = {\left(\frac{3}{2}\right)}^{2} = \frac{9}{4}$