Question

The areas of two circles are in the ratio 49:81. What is the ratio of their circumferences?

• A. 7:9
• B. 9:7
• C. 14:9
• D. 7:18

Answer 1

The correct option is A 7:9

Given, the ratio of areas of two circles is 49:81.

Let the radii of the two cicles be $r_1$ and $r_2$ respectively.

So, the area of first circle
$=\pi r_1^2$

The area of the second circle
$=\pi r_2^2$

Ratio of their areas = 49:81

$\therefore$ $\pi r_1^2$:$\pi r_1^2$ = 49:81

$\Rightarrow$ $r_1^2$:$r_2^2$ = 49:81

$\Rightarrow$ $r_1$:$r_2$ = 7:9

Let the radii of the two circles be $7x$ and $9x$.

So, the circumference of first circle
= 2π$r_1$ = 2π x 7$x$ = 14π$x$

The circumference of the second circle = 2π$r_2$ = 2π x 9$x$ = 18 π $x$

The ratio of the circumferences of the two circles
= 14π$x$:18π$x$
= 14:18
= 7:9