Question

Find the ratio of the radii of two circles if the ratio of their areas is 4:9.
Find the ratio of the radii of two circles if the ratio of their areas is 4:9.
@Mathematics

Answer 1

2/3

Answer 2

how did you get that?

Answer 3

(pi*r1^2/pi*r2^2)=4/9==>(r1/r2)^2=4/9===>(r1/r2)=2/3

Answer 4

\[A_1=\pi r_1 ^2=4k \]

\[A_2=pir^2_2=9k\]

\[A_1 :A_2 => 4:9 \text{ since (4k)/(9k)=4/9}\]


\[r^2_1= \frac{4k}{\pi} => r_1=2 \sqrt{\frac{k}{\pi}}\]

\[r_2^2=\frac{9k}{\pi} => r_2=3 \sqrt{\frac{k}{\pi}}\]
\[\frac{r_1}{r_2}=\frac{2 \sqrt{\frac{k}{\pi}}}{3 \sqrt{\frac{k}{\pi}}}=\frac{2}{3} => 2: 3 \]