A circle has a radius of 9 inches. The radius is multiplied by 23 to form a second circle. How is the ratio of the areas related to the ratio of the radii?

Step 1 r1=9 r2=9×23=6 r1r2=96=32 The area of a circle is π×r2 ⇒a1a2=π×92π×62=(96)2=(32)2=94

Explained: "A circle has a radius of 9 inches...."

Cierra Woodard

2022-02-03

A circle has a radius of 9 inches. The radius is multiplied by

\frac{2}{3}

to form a second circle. How is the ratio of the areas related to the ratio of the radii?

chicasdelperuszp

Beginner2022-02-04Added 14 answers

Step 1

r_{1} = 9

r_{2} = 9 \times \frac{2}{3} = 6

\frac{r_{1}}{r_{2}} = \frac{9}{6} = \frac{3}{2}

The area of a circle is

π \times r^{2}

\Rightarrow \frac{a_{1}}{a_{2}} = \frac{π \times 9^{2}}{π \times 6^{2}} = {(\frac{9}{6})}^{2} = {(\frac{3}{2})}^{2} = \frac{9}{4}

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