Question

Question 69

The areas of two circles are in the ratio 49 : 64. Find the ratio of their circumferences.

Answer 1

Given, the area of two circles are in the ratio 49 : 64
Area of a circle $=\pi r^2$
Let area of the first circle $=\pi r_1^2$
and area of the second circle $=\pi r_2^2$
According to the question, $\frac{49}{64}=\frac{\pi r_1^2}{\pi r_2^2}$
$\Rightarrow \frac{49}{64}=\frac{r_1^2}{r_2^2}$
$\Rightarrow \frac{(7{)}^2}{(8{)}^2}=\frac{r_1^2}{r_2^2}\Rightarrow {\left(\frac{7}{8}\right)}^2={\left(\frac{r_1}{r_2}\right)}^2$
$\therefore r_1=7$ and $r_2=8$
The ratio of circumferences of these two circles
$=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}=\frac{7}{8}$ [$\because$ circumference of circle $=2\pi r$]
Hence, required ratio is 7 : 8