Question

The areas of two circles are in the ratio 64:100. Find the ratio of their circumferences. ​

Answer 1

Answer:

the ratio of circumference is 8:10

Step-by-step explanation:

Ratio of the area of two circles given = 64:100

Area of circle = πr2

now,

area of first circle=64

area of second circle=100

⇒

64/100

⇒

(8)^2/(10)^2

8:10 is the ratio of circumference

Answer 2

Ratio of the area of two circles given = 64:100

Area of circle = $\pi {r}^{2}$

Area of the first circle = $\pi {r1}^{2}$

Area of the second circle = $\pi {r2}^{2}$

Now,

$\frac{64}{100} = \frac{\pi {r1}^{2} }{\pi {r2}^{2} } \\ \frac{ {(64)}^{2} }{ {(100)}^{2} } = \frac{ {r1}^{2} }{ {r2}^{2} } \\ ({ \frac{16}{25} )}^{2} = ( { \frac{r1}{r2} })^{2} \\ \\ \\ \\ r1 = 16 \\ r2 = 25$

The ratio of circumferences of these two circles-

$\frac{2\pi \: r1} {2\pi \: r2} \\ = \frac{r1}{r2} = \frac{16}{25}$

= 16:25